Question

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

Responses

{17.84,−13.84}

left brace 17.84 comma negative 13.84 right brace

{253,−325}

left brace 253 comma negative 325 right brace

{−19,−53}

left brace negative 19 comma negative 53 right brace

{53,19}

Answer 1

To solve the equation \((x+36)^2 - 38 = 251\), we first simplify it step by step.

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

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

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

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

Thus, the solution set is:
\[
\{-19, -53\}
\]

The correct response is:
\(\{−19,−53\}\)