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

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

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Numerical solution:

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The solution

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       2           2
(x - 5)  = (x + 10) 
$$\left(x - 5\right)^{2} = \left(x + 10\right)^{2}$$
Detail solution
Given the equation:
(x-5)^2 = (x+10)^2

Expand expressions:
25 + x^2 - 10*x = (x+10)^2

(x-5)^2 = 100 + x^2 + 20*x

Reducing, you get:
-75 - 30*x = 0

Move free summands (without x)
from left part to right part, we given:
$$- 30 x = 75$$
Divide both parts of the equation by -30
x = 75 / (-30)

We get the answer: x = -5/2
The graph
Rapid solution [src]
x1 = -5/2
$$x_{1} = - \frac{5}{2}$$
x1 = -5/2
Sum and product of roots [src]
sum
-5/2
$$- \frac{5}{2}$$
=
-5/2
$$- \frac{5}{2}$$
product
-5/2
$$- \frac{5}{2}$$
=
-5/2
$$- \frac{5}{2}$$
-5/2
Numerical answer [src]
x1 = -2.5
x1 = -2.5
The graph
(x-5)^2=(x+10)^2 equation