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x*x+2*a*x+b=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución numérica:

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Solución

Ha introducido [src] 
x*x + 2*a*x + b = 0
b+(2ax+xx)=0b + \left(2 a x + x x\right) = 0
Simplificar
Solución detallada
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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=1a = 1
b=2ab = 2 a
c=bc = b
, entonces
D = b^2 - 4 * a * c = 

(2*a)^2 - 4 * (1) * (b) = -4*b + 4*a^2

La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

o
x1=−a+4a2−4b2x_{1} = - a + \frac{\sqrt{4 a^{2} - 4 b}}{2}
x2=−a−4a2−4b2x_{2} = - a - \frac{\sqrt{4 a^{2} - 4 b}}{2}
Teorema de Cardano-Vieta
es ecuación cuadrática reducida
px+q+x2=0p x + q + x^{2} = 0
donde
p=bap = \frac{b}{a}
p=2ap = 2 a
q=caq = \frac{c}{a}
q=bq = b
Fórmulas de Cardano-Vieta
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−2ax_{1} + x_{2} = - 2 a
x1x2=bx_{1} x_{2} = b
Gráfica
Respuesta rápida [src] 
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                |            /                                                      2     /     /                          2        2           \\|      /                                                      2     /     /                          2        2           \\
                |         4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||   4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/|
x1 = -re(a) + I*|-im(a) - \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *sin|------------------------------------------------------|| - \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *cos|------------------------------------------------------|
                \                                                                         \                          2                           //                                                                   \                          2                           /
x1=i(−(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−im⁡(a))−(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−re⁡(a)x_{1} = i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} 
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                |            /                                                      2     /     /                          2        2           \\|      /                                                      2     /     /                          2        2           \\
                |         4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||   4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/|
x2 = -re(a) + I*|-im(a) + \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *sin|------------------------------------------------------|| + \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *cos|------------------------------------------------------|
                \                                                                         \                          2                           //                                                                   \                          2                           /
x2=i((2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−im⁡(a))+(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−re⁡(a)x_{2} = i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)} 
x2 = i*(((2*re(a)*im(a) - im(b))^2 + (re(a)^2 - re(b) - im(a)^2)^2)^(1/4)*sin(atan2(2*re(a)*im(a) - im(b, re(a)^2 - re(b) - im(a)^2)/2) - im(a)) + ((2*re(a)*im(a) - im(b))^2 + (re(a)^2 - re(b) - im(a)^2)^2)^(1/4)*cos(atan2(2*re(a)*im(a) - im(b), re(a)^2 - re(b) - im(a)^2)/2) - re(a))
Suma y producto de raíces [src] 
suma
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           |            /                                                      2     /     /                          2        2           \\|      /                                                      2     /     /                          2        2           \\              |            /                                                      2     /     /                          2        2           \\|      /                                                      2     /     /                          2        2           \\
           |         4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||   4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/|              |         4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||   4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/|
-re(a) + I*|-im(a) - \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *sin|------------------------------------------------------|| - \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *cos|------------------------------------------------------| + -re(a) + I*|-im(a) + \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *sin|------------------------------------------------------|| + \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *cos|------------------------------------------------------|
           \                                                                         \                          2                           //                                                                   \                          2                           /              \                                                                         \                          2                           //                                                                   \                          2                           /
(i(−(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−im⁡(a))−(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−re⁡(a))+(i((2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−im⁡(a))+(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−re⁡(a))\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) + \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) 
=
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             |            /                                                      2     /     /                          2        2           \\|     |            /                                                      2     /     /                          2        2           \\|
             |         4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||     |         4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||
-2*re(a) + I*|-im(a) + \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *sin|------------------------------------------------------|| + I*|-im(a) - \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *sin|------------------------------------------------------||
             \                                                                         \                          2                           //     \                                                                         \                          2                           //
i(−(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−im⁡(a))+i((2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−im⁡(a))−2re⁡(a)i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) - 2 \operatorname{re}{\left(a\right)} 
producto
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|           |            /                                                      2     /     /                          2        2           \\|      /                                                      2     /     /                          2        2           \\| |           |            /                                                      2     /     /                          2        2           \\|      /                                                      2     /     /                          2        2           \\|
|           |         4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||   4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/|| |           |         4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||   4 /                          2   /  2        2           \      |atan2\-im(b) + 2*im(a)*re(a), re (a) - im (a) - re(b)/||
|-re(a) + I*|-im(a) - \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *sin|------------------------------------------------------|| - \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *cos|------------------------------------------------------||*|-re(a) + I*|-im(a) + \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *sin|------------------------------------------------------|| + \/   (-im(b) + 2*im(a)*re(a))  + \re (a) - im (a) - re(b)/  *cos|------------------------------------------------------||
\           \                                                                         \                          2                           //                                                                   \                          2                           // \           \                                                                         \                          2                           //                                                                   \                          2                           //
(i(−(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−im⁡(a))−(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−re⁡(a))(i((2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24sin⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−im⁡(a))+(2re⁡(a)im⁡(a)−im⁡(b))2+((re⁡(a))2−re⁡(b)−(im⁡(a))2)24cos⁡(atan2⁡(2re⁡(a)im⁡(a)−im⁡(b),(re⁡(a))2−re⁡(b)−(im⁡(a))2)2)−re⁡(a))\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(b\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(b\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) 
=
I*im(b) + re(b)
re⁡(b)+iim⁡(b)\operatorname{re}{\left(b\right)} + i \operatorname{im}{\left(b\right)} 
i*im(b) + re(b)
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