Question

Which option contains the solution set for the value of k in the equation 7+2k2=25
?(1 point)
Responses

{3}
left brace 3 right brace

{−3,3}
left brace negative 3 comma 3 right brace

∅
empty set

{−9,9}

Answer 1

To solve the equation \(7 + 2k^2 = 25\), first, we can isolate the term involving \(k\):

1. Subtract \(7\) from both sides:
\[
2k^2 = 25 - 7
\]
\[
2k^2 = 18
\]

2. Now divide both sides by \(2\):
\[
k^2 = \frac{18}{2}
\]
\[
k^2 = 9
\]

3. Now take the square root of both sides:
\[
k = \pm 3
\]

So the solution set for the value of \(k\) is \(\{-3, 3\}\).

Therefore, the correct response is:

\(\{-3, 3\}\)