Question

Solve the quadratic equation (x−4)2=25 . Enter both solutions for x :(2 points)

Answer 1

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

1. Taking the square root:
\[
x - 4 = ±5
\]

2. This gives us two equations to solve:
- For \(x - 4 = 5\):
\[
x = 5 + 4 = 9
\]
- For \(x - 4 = -5\):
\[
x = -5 + 4 = -1
\]

Thus, the two solutions for \(x\) are:
\[
x = 9 \quad \text{and} \quad x = -1
\]

Final answers:
- \(x = 9\)
- \(x = -1\)