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(x-5)=(x+10)^2

(x-5)=(x+10)^2 equation

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Numerical solution:

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The solution

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                2
x - 5 = (x + 10) 
$$x - 5 = \left(x + 10\right)^{2}$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$x - 5 = \left(x + 10\right)^{2}$$
to
$$\left(x - 5\right) - \left(x + 10\right)^{2} = 0$$
Expand the expression in the equation
$$\left(x - 5\right) - \left(x + 10\right)^{2} = 0$$
We get the quadratic equation
$$- x^{2} - 19 x - 105 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -1$$
$$b = -19$$
$$c = -105$$
, then
D = b^2 - 4 * a * c = 

(-19)^2 - 4 * (-1) * (-105) = -59

Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)

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

or
$$x_{1} = - \frac{19}{2} - \frac{\sqrt{59} i}{2}$$
$$x_{2} = - \frac{19}{2} + \frac{\sqrt{59} i}{2}$$
The graph
Sum and product of roots [src]
sum
           ____              ____
  19   I*\/ 59      19   I*\/ 59 
- -- - -------- + - -- + --------
  2       2         2       2    
$$\left(- \frac{19}{2} - \frac{\sqrt{59} i}{2}\right) + \left(- \frac{19}{2} + \frac{\sqrt{59} i}{2}\right)$$
=
-19
$$-19$$
product
/           ____\ /           ____\
|  19   I*\/ 59 | |  19   I*\/ 59 |
|- -- - --------|*|- -- + --------|
\  2       2    / \  2       2    /
$$\left(- \frac{19}{2} - \frac{\sqrt{59} i}{2}\right) \left(- \frac{19}{2} + \frac{\sqrt{59} i}{2}\right)$$
=
105
$$105$$
105
Rapid solution [src]
                ____
       19   I*\/ 59 
x1 = - -- - --------
       2       2    
$$x_{1} = - \frac{19}{2} - \frac{\sqrt{59} i}{2}$$
                ____
       19   I*\/ 59 
x2 = - -- + --------
       2       2    
$$x_{2} = - \frac{19}{2} + \frac{\sqrt{59} i}{2}$$
x2 = -19/2 + sqrt(59)*i/2
Numerical answer [src]
x1 = -9.5 + 3.8405728739343*i
x2 = -9.5 - 3.8405728739343*i
x2 = -9.5 - 3.8405728739343*i
The graph
(x-5)=(x+10)^2 equation