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

To solve the equation \((x + 36)^2 - 38 = 251\), we first isolate the squared term:

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

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 \(x\) in both cases:
- For \(x + 36 = 17\):
\[
x = 17 - 36 = -19
\]

- For \(x + 36 = -17\):
\[
x = -17 - 36 = -53
\]

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

The answer is \(\{-19, -53\}\).