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To solve the quadratic equation \((x - 4)^2 = 25\) using square roots, we can follow these steps:
1. **Take the square root of both sides:**
\[
x - 4 = \pm 5
\]
This gives us two equations to solve:
- \(x - 4 = 5\)
- \(x - 4 = -5\)
2. **Solve each equation:**
For \(x - 4 = 5\):
\[
x = 5 + 4 = 9
\]
For \(x - 4 = -5\):
\[
x = -5 + 4 = -1
\]
3. **The solutions are:**
\[
x = 9 \quad \text{and} \quad x = -1
\]
Thus, the solutions to the equation \((x - 4)^2 = 25\) are \(\{-1, 9\}\).
The correct response is:
**{−1, 9}**