Question

What is the solution to the equation (x - 5)^2 = x^2 + 25?

A) x = 0
B) x = 5
C) x = 6
D) x = -6

Answer 1

The solution to the equation (x - 5)^2 = x^2 + 25 is A) x = 0. This is found by expanding the squared term, simplifying, and then isolating x.

Step-by-step explanation:

To solve the equation (x - 5)^2 = x^2 + 25, let's first expand the left side of the equation:

(x - 5)(x - 5) = x^2 - 10x + 25

Now, we have x^2 - 10x + 25 = x^2 + 25. If we subtract x^2 and 25 from both sides of the equation, we get:

-10x = 0

Divide both sides by -10, we find x = 0.

Therefore, the solution to the equation (x - 5)^2 = x^2 + 25 is x = 0, which matches option A) x = 0.