Question

Using square roots, solve the equation (x - 4)² = 1 for the values of x.

Answer 1

To solve the equation (x - 4)² = 1, we take the square root of both sides, leading to two solutions: x = 5 and x = 3.

Step-by-step explanation:

To solve the equation (x - 4)² = 1 using square roots, we first take the square root of both sides of the equation, resulting in two possible solutions since the square root of 1 is both 1 and -1. Hence, we have:

x - 4 = 1 and x - 4 = -1

Solving each equation for x gives:

1. x - 4 = 1 leads to x = 5
2. x - 4 = -1 leads to x = 3

Thus, the equation (x - 4)² = 1 has two solutions for the values of x: x = 5 and x = 3.