Question

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

{253,−325}
left brace 253 comma negative 325 right brace

{53,19}
left brace 53 comma 19 right brace

{−19,−53}
left brace negative 19 comma negative 53 right brace

{17.84,−13.84}

Answer 1

To solve the quadratic equation \((x + 36)^2 - 38 = 251\) using square roots, 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:
\[
x + 36 = \pm 17
\]

3. **Solve for \(x\) in both cases:**

- For the positive case:
\[
x + 36 = 17
\]
Subtract 36 from both sides:
\[
x = 17 - 36 = -19
\]

- For the negative case:
\[
x + 36 = -17
\]
Subtract 36 from both sides:
\[
x = -17 - 36 = -53
\]

4. **Conclusion:**
The solutions to the equation are:
\[
\{ -19, -53 \}
\]

Thus, the correct response is:

\(\{ -19, -53 \}\)