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

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

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

{17.84,−13.84}

Answers

Answered by GPT-4o mini
To solve the given quadratic equation \((x + 36)^2 - 38 = 251\), we first simplify and isolate the square:

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 \(x\) in both cases:
- For \(x + 36 = 17\):
\[
x = 17 - 36
\]
\[
x = -19
\]

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

Thus, the solutions are:
\[
\{ -19, -53 \}
\]

The correct response is:

\[
\{ -19, -53 \} \text{ (left brace negative 19 comma negative 53 right brace)}
\]
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions