Question

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

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

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

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

{17.84,−13.84}

Answer 1

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

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

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

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

4. **Final solutions:**
\[
x = -19 \quad \text{and} \quad x = -53
\]

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

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