Which option contains the solution set for the value of k in the equation 7+2k2=25

Question

?(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}

Answer 1

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:

\({ -3, 3 }\)