Which option contains the solution set for the value of k in the equation 7+2k2=25
?(1 point)
Responses
{−3,3}
left brace negative 3 comma 3 right brace
∅
empty set
{−9,9}
left brace negative 9 comma 9 right brace
{3}
?(1 point)
Responses
{−3,3}
left brace negative 3 comma 3 right brace
∅
empty set
{−9,9}
left brace negative 9 comma 9 right brace
{3}
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \( 7 + 2k^2 = 25 \), we first isolate the term with \( k^2 \):
1. Subtract 7 from both sides:
\[
2k^2 = 25 - 7
\]
\[
2k^2 = 18
\]
2. Divide both sides by 2:
\[
k^2 = \frac{18}{2}
\]
\[
k^2 = 9
\]
3. Take the square root of both sides:
\[
k = \pm 3
\]
Thus, the solution set for the value of \( k \) is
\[
\{ -3, 3 \}
\]
Therefore, the correct response is:
\(\{ -3, 3 \}\)
1. Subtract 7 from both sides:
\[
2k^2 = 25 - 7
\]
\[
2k^2 = 18
\]
2. Divide both sides by 2:
\[
k^2 = \frac{18}{2}
\]
\[
k^2 = 9
\]
3. Take the square root of both sides:
\[
k = \pm 3
\]
Thus, the solution set for the value of \( k \) is
\[
\{ -3, 3 \}
\]
Therefore, the correct response is:
\(\{ -3, 3 \}\)
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