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

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

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

{−19,−53}

Answer 1

To solve the quadratic equation \((x + 36)^2 - 38 = 251\), let's first isolate the term with the square.

1. Add 38 to both sides:

\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]

2. Next, take the square root of both sides:

\[
x + 36 = \pm \sqrt{289}
\]
\[
x + 36 = \pm 17
\]

3. Now, we solve for \(x\) in two cases:

**Case 1:** \(x + 36 = 17\)

\[
x = 17 - 36
\]
\[
x = -19
\]

**Case 2:** \(x + 36 = -17\)

\[
x = -17 - 36
\]
\[
x = -53
\]

4. Therefore, the solutions to the equation are:

\[
x = -19 \quad \text{and} \quad x = -53
\]

The final solution set is:

\[
\{-19, -53\}
\]

So, the correct response is:

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