Solve the quadratic equation below using square roots. (x − 4)^2 = 25

Question

A) {-1, 9}
B) {-2, 6}
C) {-√29, √29}
D) {-3, 7}

Answer 1

To solve the quadratic equation \((x - 4)^2 = 25\) using square roots, we start by taking the square root of both sides of the equation.

1. Rewrite the equation: \[ (x - 4)^2 = 25 \]

2. Take the square root of both sides: \[ x - 4 = \pm 5 \]

This gives us two separate equations to solve:

First Equation: \[ x - 4 = 5 \] Adding 4 to both sides: \[ x = 5 + 4 = 9 \]

Second Equation: \[ x - 4 = -5 \] Adding 4 to both sides: \[ x = -5 + 4 = -1 \]

Therefore, the solutions to the equation \((x - 4)^2 = 25\) are: \[ x = 9 \quad \text{and} \quad x = -1 \]

The solution set can be written as: \[ { -1, 9 } \]

Thus, the correct answer is: A) {-1, 9}.