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

To solve the equation \((x + 36)^2 - 38 = 251\), let's follow these steps:

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

2. **Take the square root of both sides**:
\[
x + 36 = \pm \sqrt{289}
\]
Since \( \sqrt{289} = 17 \), we have:
\[
x + 36 = 17 \quad \text{or} \quad x + 36 = -17
\]

3. **Solve for \(x\)**:
- For \(x + 36 = 17\):
\[
x = 17 - 36 = -19
\]
- For \(x + 36 = -17\):
\[
x = -17 - 36 = -53
\]

So, the solutions to the quadratic equation are:
\[
\{ -19, -53 \}
\]

Thus, the correct response is:
\[
\{ -19, -53 \}
\]