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:

• \(x = 9\)
• \(x = -1\)