Question

Find the solution(s) to (x-4)² = 64.

a. x = 8
b. x = –4
c. x = –12
d. x = –8
e. x = 4

Answer 1

The solutions to the equation (x-4)² = 64 are obtained by taking the square root of both sides, leading to two possible solutions, x = 12 and x = -4. Option b

Step-by-step explanation:

To solve the quadratic equation (x-4)² = 64, we take the square root of both sides of the equation. This results in two potential solutions because the square root of a number can be either positive or negative:

√(x-4)² = ±64 ⇒ x-4 = ±8 ⇒ x = 4 ± 8

Adding 8: x = 4 + 8 ⇒ x = 12

Subtracting 8: x = 4 - 8 ⇒ x = -4

Therefore, the solutions are x = 12 and x = -4. Option b