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}
.(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:
\[
\{ -19, -53 \} \text{ (left brace negative 19 comma negative 53 right brace)}
\]
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:
\[
\{ -19, -53 \} \text{ (left brace negative 19 comma negative 53 right brace)}
\]
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