Solve the quadratic equation below using square roots.

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

1. Take the square root of both sides of the equation:

\[
x - 4 = \pm 5
\]

2. Solve for \(x\) by separating the two cases:

**Case 1:**
\[
x - 4 = 5 \\
x = 5 + 4 = 9
\]

**Case 2:**
\[
x - 4 = -5 \\
x = -5 + 4 = -1
\]

Thus, the solutions are:

\[
x = 9 \quad \text{and} \quad x = -1
\]

So the answer is \(\{-1, 9\}\).