Solve the following quadratic equation using square roots: (x+36)2−38=251 .(1 point)

To solve the quadratic equation \((x + 36)^2 - 38 = 251\) using square roots, follow these steps:

1. **Add 38 to both sides**:
\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]

2. **Take the square root of both sides**:
\[
x + 36 = \pm \sqrt{289}
\]
\[
x + 36 = \pm 17
\]

3. **Consider both cases**:
- For \(x + 36 = 17\):
\[
x = 17 - 36 = -19
\]
- For \(x + 36 = -17\):
\[
x = -17 - 36 = -53
\]

4. **Thus, the solutions are**:
\[
x = -19 \quad \text{and} \quad x = -53
\]

The final solutions are \(\{-19, -53\}\).

So, the correct response is:
\[
\{−19,−53\}
\]