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- 2*x^2+(a+43)*x+a^2-29a-10=0
2*x^2+(a+43)*x-a^2-29a-10=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 2*x + (a + 43)*x - a - 29*a - 10 = 0
$$\left(- 29 a + \left(- a^{2} + \left(2 x^{2} + x \left(a + 43\right)\right)\right)\right) - 10 = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$\left(- 29 a + \left(- a^{2} + \left(2 x^{2} + x \left(a + 43\right)\right)\right)\right) - 10 = 0$$
Obtenemos la ecuación cuadrática
$$- a^{2} + a x - 29 a + 2 x^{2} + 43 x - 10 = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 2$$
$$b = a + 43$$
$$c = - a^{2} - 29 a - 10$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - \frac{a}{4} + \frac{\sqrt{8 a^{2} + 232 a + \left(a + 43\right)^{2} + 80}}{4} - \frac{43}{4}$$
$$x_{2} = - \frac{a}{4} - \frac{\sqrt{8 a^{2} + 232 a + \left(a + 43\right)^{2} + 80}}{4} - \frac{43}{4}$$
$$\left(- 29 a + \left(- a^{2} + \left(2 x^{2} + x \left(a + 43\right)\right)\right)\right) - 10 = 0$$
Obtenemos la ecuación cuadrática
$$- a^{2} + a x - 29 a + 2 x^{2} + 43 x - 10 = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 2$$
$$b = a + 43$$
$$c = - a^{2} - 29 a - 10$$
, entonces
D = b^2 - 4 * a * c =
(43 + a)^2 - 4 * (2) * (-10 - a^2 - 29*a) = 80 + (43 + a)^2 + 8*a^2 + 232*a
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \frac{a}{4} + \frac{\sqrt{8 a^{2} + 232 a + \left(a + 43\right)^{2} + 80}}{4} - \frac{43}{4}$$
$$x_{2} = - \frac{a}{4} - \frac{\sqrt{8 a^{2} + 232 a + \left(a + 43\right)^{2} + 80}}{4} - \frac{43}{4}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- 29 a + \left(- a^{2} + \left(2 x^{2} + x \left(a + 43\right)\right)\right)\right) - 10 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- \frac{a^{2}}{2} - \frac{29 a}{2} + x^{2} + \frac{x \left(a + 43\right)}{2} - 5 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{a}{2} + \frac{43}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{a^{2}}{2} - \frac{29 a}{2} - 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{a}{2} - \frac{43}{2}$$
$$x_{1} x_{2} = - \frac{a^{2}}{2} - \frac{29 a}{2} - 5$$
$$\left(- 29 a + \left(- a^{2} + \left(2 x^{2} + x \left(a + 43\right)\right)\right)\right) - 10 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- \frac{a^{2}}{2} - \frac{29 a}{2} + x^{2} + \frac{x \left(a + 43\right)}{2} - 5 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{a}{2} + \frac{43}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{a^{2}}{2} - \frac{29 a}{2} - 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{a}{2} - \frac{43}{2}$$
$$x_{1} x_{2} = - \frac{a^{2}}{2} - \frac{29 a}{2} - 5$$
Gráfica
Suma y producto de raíces
[src]
suma
/ ___________________________________________________________________________ \ ___________________________________________________________________________ / ___________________________________________________________________________ \ ___________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/| | 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|
| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *sin|-------------------------------------------------------------------------|| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *cos|-------------------------------------------------------------------------| | \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *sin|-------------------------------------------------------------------------|| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *cos|-------------------------------------------------------------------------|
43 re(a) | im(a) \ 2 /| \ 2 / 43 re(a) | im(a) \ 2 /| \ 2 /
- -- - ----- + I*|- ----- - --------------------------------------------------------------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------------------------------------------------------------- + - -- - ----- + I*|- ----- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------
4 4 \ 4 4 / 4 4 4 \ 4 4 / 4
$$\left(i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{im}{\left(a\right)}}{4}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{re}{\left(a\right)}}{4} - \frac{43}{4}\right) + \left(i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{im}{\left(a\right)}}{4}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{re}{\left(a\right)}}{4} - \frac{43}{4}\right)$$
=
/ ___________________________________________________________________________ \ / ___________________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| | 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/||
| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *sin|-------------------------------------------------------------------------|| | \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *sin|-------------------------------------------------------------------------||
43 re(a) | im(a) \ 2 /| | im(a) \ 2 /|
- -- - ----- + I*|- ----- - --------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ----- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|
2 2 \ 4 4 / \ 4 4 /
$$i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{im}{\left(a\right)}}{4}\right) + i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{im}{\left(a\right)}}{4}\right) - \frac{\operatorname{re}{\left(a\right)}}{2} - \frac{43}{2}$$
producto
/ / ___________________________________________________________________________ \ ___________________________________________________________________________ \ / / ___________________________________________________________________________ \ ___________________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| | | 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| | | \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *sin|-------------------------------------------------------------------------|| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *cos|-------------------------------------------------------------------------|| | | \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *sin|-------------------------------------------------------------------------|| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *cos|-------------------------------------------------------------------------|| | 43 re(a) | im(a) \ 2 /| \ 2 /| | 43 re(a) | im(a) \ 2 /| \ 2 /| |- -- - ----- + I*|- ----- - --------------------------------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- -- - ----- + I*|- ----- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 4 4 \ 4 4 / 4 / \ 4 4 \ 4 4 / 4 /
$$\left(i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{im}{\left(a\right)}}{4}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{re}{\left(a\right)}}{4} - \frac{43}{4}\right) \left(i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{im}{\left(a\right)}}{4}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{re}{\left(a\right)}}{4} - \frac{43}{4}\right)$$
=
2 2
im (a) 29*re(a) re (a) 29*I*im(a)
-5 + ------ - -------- - ------ - ---------- - I*im(a)*re(a)
2 2 2 2
$$- \frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{2} - i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \frac{29 \operatorname{re}{\left(a\right)}}{2} + \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{2} - \frac{29 i \operatorname{im}{\left(a\right)}}{2} - 5$$
-5 + im(a)^2/2 - 29*re(a)/2 - re(a)^2/2 - 29*i*im(a)/2 - i*im(a)*re(a)
Respuesta rápida
[src]
/ ___________________________________________________________________________ \ ___________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|
| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *sin|-------------------------------------------------------------------------|| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *cos|-------------------------------------------------------------------------|
43 re(a) | im(a) \ 2 /| \ 2 /
x1 = - -- - ----- + I*|- ----- - --------------------------------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------------------------------------------------------------------------------
4 4 \ 4 4 / 4
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{im}{\left(a\right)}}{4}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{re}{\left(a\right)}}{4} - \frac{43}{4}$$
/ ___________________________________________________________________________ \ ___________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|| 4 / 2 / 2 2 \ |atan2\318*im(a) + 18*im(a)*re(a), 1929 - 9*im (a) + 9*re (a) + 318*re(a)/|
| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *sin|-------------------------------------------------------------------------|| \/ (318*im(a) + 18*im(a)*re(a)) + \1929 - 9*im (a) + 9*re (a) + 318*re(a)/ *cos|-------------------------------------------------------------------------|
43 re(a) | im(a) \ 2 /| \ 2 /
x2 = - -- - ----- + I*|- ----- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------
4 4 \ 4 4 / 4
$$x_{2} = i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{im}{\left(a\right)}}{4}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 318 \operatorname{im}{\left(a\right)},9 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 318 \operatorname{re}{\left(a\right)} - 9 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1929 \right)}}{2} \right)}}{4} - \frac{\operatorname{re}{\left(a\right)}}{4} - \frac{43}{4}$$
x2 = i*(((18*re(a)*im(a) + 318*im(a))^2 + (9*re(a)^2 + 318*re(a) - 9*im(a)^2 + 1929)^2)^(1/4)*sin(atan2(18*re(a)*im(a) + 318*im(a, 9*re(a)^2 + 318*re(a) - 9*im(a)^2 + 1929)/2)/4 - im(a)/4) + ((18*re(a)*im(a) + 318*im(a))^2 + (9*re(a)^2 + 318*re(a) - 9*im(a)^2 + 1929)^2)^(1/4)*cos(atan2(18*re(a)*im(a) + 318*im(a), 9*re(a)^2 + 318*re(a) - 9*im(a)^2 + 1929)/2)/4 - re(a)/4 - 43/4)