Question

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

{17.84,−13.84}
{
17.84
,
−
13.84
}
left brace 17.84 comma negative 13.84 right brace

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

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

{53,19}

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 \(\sqrt{289} = 17\):
\[
x + 36 = 17 \quad \text{or} \quad x + 36 = -17
\]

3. **Solve for \(x\)** in both cases:
1. For \(x + 36 = 17\):
\[
x = 17 - 36
\]
\[
x = -19
\]

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

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

Therefore, the solution set is \(\{ -19, -53 \}\).

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