Question

Solve for (x-4)^2 = 25 and find the sum of the solutions

A. -8
B. -6
C. 6
D. 8

Answer 1

The equation (x-4)^2 = 25 has two solutions, x = 9 and x = -1. The sum of these two solutions is 8, which corresponds to answer choice D.

Step-by-step explanation:

To solve for x in the equation (x-4)² = 25, we take the square root of both sides of the equation:

• x - 4 = ±5
• x = 4 ± 5

This results in two possible solutions for x:

• x = 4 + 5
• x = 4 - 5

Which simplifies to:

• x = 9
• x = -1

The sum of the solutions is:

9 + (-1) = 8

Thus, the sum of the solutions is 8, which corresponds to answer choice D.