Solve the quadratic equation below using square roots (x - 4) ^ 2 = 25 (1 point)

Answer 1

To solve the quadratic equation \((x - 4)^2 = 25\) using square roots, follow these steps:

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

2. This gives us two equations to solve: \[ x - 4 = 5 \quad \text{and} \quad x - 4 = -5 \]

3. Solve the first equation: \[ x - 4 = 5 \implies x = 5 + 4 \implies x = 9 \]

4. Solve the second equation: \[ x - 4 = -5 \implies x = -5 + 4 \implies x = -1 \]

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