(x+5)²=(x-10)² equation

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

$$\left(x + 5\right)^{2} = \left(x - 10\right)^{2}$$

Simplify

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

Plot the graph f1(x)

Plot the graph f2(x)

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