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sqrt(1-2x)=a-11absolute(x) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
  _________             
\/ 1 - 2*x  = a - 11*|x|
$$\sqrt{1 - 2 x} = a - 11 \left|{x}\right|$$
Solución detallada
Para cada expresión dentro del módulo en la ecuación
admitimos los casos cuando la expresión correspondiente es ">= 0" o "< 0",
resolvemos las ecuaciones obtenidas.

1.
$$x \geq 0$$
o
$$0 \leq x \wedge x < \infty$$
obtenemos la ecuación
$$- a + 11 x + \sqrt{1 - 2 x} = 0$$
simplificamos, obtenemos
$$- a + 11 x + \sqrt{1 - 2 x} = 0$$
la resolución en este intervalo:
$$x_{1} = \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{2} = \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$

2.
$$x < 0$$
o
$$-\infty < x \wedge x < 0$$
obtenemos la ecuación
$$- a + 11 \left(- x\right) + \sqrt{1 - 2 x} = 0$$
simplificamos, obtenemos
$$- a - 11 x + \sqrt{1 - 2 x} = 0$$
la resolución en este intervalo:
$$x_{3} = - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
$$x_{4} = - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$


Entonces la respuesta definitiva es:
$$x_{1} = \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{2} = \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{3} = - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
$$x_{4} = - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
Gráfica
Suma y producto de raíces [src]
suma
    //               ____________                   ___   ___________    \     //               ____________                   ___   ___________    \       //               ____________                   ___   ___________    \     //               ____________                   ___   ___________    \       //          ____________                        ___   ___________     \     //          ____________                        ___   ___________     \       //               ____________                     ___   ___________     \     //               ____________                     ___   ___________     \
    ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |     ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |       ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |     ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |       ||   1    \/ 122 - 22*a    a        1    a    \/ 2 *\/ 61 - 11*a      |     ||   1    \/ 122 - 22*a    a        1    a    \/ 2 *\/ 61 - 11*a      |       ||   1    a    \/ 122 - 22*a          1    a    \/ 2 *\/ 61 - 11*a      |     ||   1    a    \/ 122 - 22*a          1    a    \/ 2 *\/ 61 - 11*a      |
    ||- --- - -- - --------------  for --- + -- + ------------------- > 0|     ||- --- - -- - --------------  for --- + -- + ------------------- > 0|       ||- --- - -- + --------------  for --- + -- - ------------------- > 0|     ||- --- - -- + --------------  for --- + -- - ------------------- > 0|       ||- --- - -------------- + --  for --- - -- + ------------------- <= 0|     ||- --- - -------------- + --  for --- - -- + ------------------- <= 0|       ||- --- + -- + --------------  for - --- + -- + ------------------- >= 0|     ||- --- + -- + --------------  for - --- + -- + ------------------- >= 0|
I*im|<  121   11        121            121   11           121            | + re|<  121   11        121            121   11           121            | + I*im|<  121   11        121            121   11           121            | + re|<  121   11        121            121   11           121            | + I*im|<  121        121         11      121   11           121             | + re|<  121        121         11      121   11           121             | + I*im|<  121   11        121              121   11           121             | + re|<  121   11        121              121   11           121             |
    ||                                                                   |     ||                                                                   |       ||                                                                   |     ||                                                                   |       ||                                                                    |     ||                                                                    |       ||                                                                      |     ||                                                                      |
    ||            nan                            otherwise               |     ||            nan                            otherwise               |       ||            nan                            otherwise               |     ||            nan                            otherwise               |       ||            nan                             otherwise               |     ||            nan                             otherwise               |       ||            nan                              otherwise                |     ||            nan                              otherwise                |
    \\                                                                   /     \\                                                                   /       \\                                                                   /     \\                                                                   /       \\                                                                    /     \\                                                                    /       \\                                                                      /     \\                                                                      /
$$\left(\left(\left(\operatorname{re}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
    //               ____________                   ___   ___________    \       //               ____________                   ___   ___________    \       //          ____________                        ___   ___________     \       //               ____________                     ___   ___________     \     //               ____________                   ___   ___________    \     //               ____________                   ___   ___________    \     //          ____________                        ___   ___________     \     //               ____________                     ___   ___________     \
    ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |       ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |       ||   1    \/ 122 - 22*a    a        1    a    \/ 2 *\/ 61 - 11*a      |       ||   1    a    \/ 122 - 22*a          1    a    \/ 2 *\/ 61 - 11*a      |     ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |     ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |     ||   1    \/ 122 - 22*a    a        1    a    \/ 2 *\/ 61 - 11*a      |     ||   1    a    \/ 122 - 22*a          1    a    \/ 2 *\/ 61 - 11*a      |
    ||- --- - -- - --------------  for --- + -- + ------------------- > 0|       ||- --- - -- + --------------  for --- + -- - ------------------- > 0|       ||- --- - -------------- + --  for --- - -- + ------------------- <= 0|       ||- --- + -- + --------------  for - --- + -- + ------------------- >= 0|     ||- --- - -- - --------------  for --- + -- + ------------------- > 0|     ||- --- - -- + --------------  for --- + -- - ------------------- > 0|     ||- --- - -------------- + --  for --- - -- + ------------------- <= 0|     ||- --- + -- + --------------  for - --- + -- + ------------------- >= 0|
I*im|<  121   11        121            121   11           121            | + I*im|<  121   11        121            121   11           121            | + I*im|<  121        121         11      121   11           121             | + I*im|<  121   11        121              121   11           121             | + re|<  121   11        121            121   11           121            | + re|<  121   11        121            121   11           121            | + re|<  121        121         11      121   11           121             | + re|<  121   11        121              121   11           121             |
    ||                                                                   |       ||                                                                   |       ||                                                                    |       ||                                                                      |     ||                                                                   |     ||                                                                   |     ||                                                                    |     ||                                                                      |
    ||            nan                            otherwise               |       ||            nan                            otherwise               |       ||            nan                             otherwise               |       ||            nan                              otherwise                |     ||            nan                            otherwise               |     ||            nan                            otherwise               |     ||            nan                             otherwise               |     ||            nan                              otherwise                |
    \\                                                                   /       \\                                                                   /       \\                                                                    /       \\                                                                      /     \\                                                                   /     \\                                                                   /     \\                                                                    /     \\                                                                      /
$$\operatorname{re}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
producto
/    //               ____________                   ___   ___________    \     //               ____________                   ___   ___________    \\ /    //               ____________                   ___   ___________    \     //               ____________                   ___   ___________    \\ /    //          ____________                        ___   ___________     \     //          ____________                        ___   ___________     \\ /    //               ____________                     ___   ___________     \     //               ____________                     ___   ___________     \\
|    ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |     ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     || |    ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |     ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     || |    ||   1    \/ 122 - 22*a    a        1    a    \/ 2 *\/ 61 - 11*a      |     ||   1    \/ 122 - 22*a    a        1    a    \/ 2 *\/ 61 - 11*a      || |    ||   1    a    \/ 122 - 22*a          1    a    \/ 2 *\/ 61 - 11*a      |     ||   1    a    \/ 122 - 22*a          1    a    \/ 2 *\/ 61 - 11*a      ||
|    ||- --- - -- - --------------  for --- + -- + ------------------- > 0|     ||- --- - -- - --------------  for --- + -- + ------------------- > 0|| |    ||- --- - -- + --------------  for --- + -- - ------------------- > 0|     ||- --- - -- + --------------  for --- + -- - ------------------- > 0|| |    ||- --- - -------------- + --  for --- - -- + ------------------- <= 0|     ||- --- - -------------- + --  for --- - -- + ------------------- <= 0|| |    ||- --- + -- + --------------  for - --- + -- + ------------------- >= 0|     ||- --- + -- + --------------  for - --- + -- + ------------------- >= 0||
|I*im|<  121   11        121            121   11           121            | + re|<  121   11        121            121   11           121            ||*|I*im|<  121   11        121            121   11           121            | + re|<  121   11        121            121   11           121            ||*|I*im|<  121        121         11      121   11           121             | + re|<  121        121         11      121   11           121             ||*|I*im|<  121   11        121              121   11           121             | + re|<  121   11        121              121   11           121             ||
|    ||                                                                   |     ||                                                                   || |    ||                                                                   |     ||                                                                   || |    ||                                                                    |     ||                                                                    || |    ||                                                                      |     ||                                                                      ||
|    ||            nan                            otherwise               |     ||            nan                            otherwise               || |    ||            nan                            otherwise               |     ||            nan                            otherwise               || |    ||            nan                             otherwise               |     ||            nan                             otherwise               || |    ||            nan                              otherwise                |     ||            nan                              otherwise                ||
\    \\                                                                   /     \\                                                                   // \    \\                                                                   /     \\                                                                   // \    \\                                                                    /     \\                                                                    // \    \\                                                                      /     \\                                                                      //
$$\left(\operatorname{re}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
/      4        4          2          2          2      2            3                                    3                                  
|1 + im (a) + re (a) - 2*re (a) + 2*im (a) - 6*im (a)*re (a) - 4*I*im (a)*re(a) - 4*I*im(a)*re(a) + 4*I*re (a)*im(a)         /     61       \
|-------------------------------------------------------------------------------------------------------------------  for And|a <= --, a > 1|
<                                                       14641                                                                \     11       /
|                                                                                                                                            
|                                                        nan                                                                 otherwise       
\                                                                                                                                            
$$\begin{cases} \frac{\left(\operatorname{re}{\left(a\right)}\right)^{4} + 4 i \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 i \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1}{14641} & \text{for}\: a \leq \frac{61}{11} \wedge a > 1 \\\text{NaN} & \text{otherwise} \end{cases}$$
Piecewise(((1 + im(a)^4 + re(a)^4 - 2*re(a)^2 + 2*im(a)^2 - 6*im(a)^2*re(a)^2 - 4*i*im(a)^3*re(a) - 4*i*im(a)*re(a) + 4*i*re(a)^3*im(a))/14641, (a <= 61/11)∧(a > 1)), (nan, True))
Respuesta rápida [src]
         //               ____________                   ___   ___________    \     //               ____________                   ___   ___________    \
         ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |     ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |
         ||- --- - -- - --------------  for --- + -- + ------------------- > 0|     ||- --- - -- - --------------  for --- + -- + ------------------- > 0|
x1 = I*im|<  121   11        121            121   11           121            | + re|<  121   11        121            121   11           121            |
         ||                                                                   |     ||                                                                   |
         ||            nan                            otherwise               |     ||            nan                            otherwise               |
         \\                                                                   /     \\                                                                   /
$$x_{1} = \operatorname{re}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
         //               ____________                   ___   ___________    \     //               ____________                   ___   ___________    \
         ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |     ||   1    a    \/ 122 + 22*a        1    a    \/ 2 *\/ 61 + 11*a     |
         ||- --- - -- + --------------  for --- + -- - ------------------- > 0|     ||- --- - -- + --------------  for --- + -- - ------------------- > 0|
x2 = I*im|<  121   11        121            121   11           121            | + re|<  121   11        121            121   11           121            |
         ||                                                                   |     ||                                                                   |
         ||            nan                            otherwise               |     ||            nan                            otherwise               |
         \\                                                                   /     \\                                                                   /
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
         //          ____________                        ___   ___________     \     //          ____________                        ___   ___________     \
         ||   1    \/ 122 - 22*a    a        1    a    \/ 2 *\/ 61 - 11*a      |     ||   1    \/ 122 - 22*a    a        1    a    \/ 2 *\/ 61 - 11*a      |
         ||- --- - -------------- + --  for --- - -- + ------------------- <= 0|     ||- --- - -------------- + --  for --- - -- + ------------------- <= 0|
x3 = I*im|<  121        121         11      121   11           121             | + re|<  121        121         11      121   11           121             |
         ||                                                                    |     ||                                                                    |
         ||            nan                             otherwise               |     ||            nan                             otherwise               |
         \\                                                                    /     \\                                                                    /
$$x_{3} = \operatorname{re}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
         //               ____________                     ___   ___________     \     //               ____________                     ___   ___________     \
         ||   1    a    \/ 122 - 22*a          1    a    \/ 2 *\/ 61 - 11*a      |     ||   1    a    \/ 122 - 22*a          1    a    \/ 2 *\/ 61 - 11*a      |
         ||- --- + -- + --------------  for - --- + -- + ------------------- >= 0|     ||- --- + -- + --------------  for - --- + -- + ------------------- >= 0|
x4 = I*im|<  121   11        121              121   11           121             | + re|<  121   11        121              121   11           121             |
         ||                                                                      |     ||                                                                      |
         ||            nan                              otherwise                |     ||            nan                              otherwise                |
         \\                                                                      /     \\                                                                      /
$$x_{4} = \operatorname{re}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((a/11 + sqrt(122 - 22*a/121 - 1/121, a/11 + sqrt(2)*sqrt(61 - 11*a)/121 - 1/121 >= 0), (nan, True))) + i*im(Piecewise((a/11 + sqrt(122 - 22*a)/121 - 1/121, a/11 + sqrt(2)*sqrt(61 - 11*a)/121 - 1/121 >= 0), (nan, True))))