1. We start with the equation:
\[
7 + 2k^2 = 25
\]
2. Next, we want to get rid of the 7 on the left side, so we subtract 7 from both sides:
\[
2k^2 = 25 - 7
\]
This gives us:
\[
2k^2 = 18
\]
3. Now, we need to make \( k^2 \) by itself, so we divide both sides by 2:
\[
k^2 = \frac{18}{2}
\]
Which simplifies to:
\[
k^2 = 9
\]
4. Finally, we take the square root of both sides to find \( k \):
\[
k = \pm 3
\]
This means that \( k \) can be either 3 or -3.
So, the answer is:
\[
k = 3 \quad \text{or} \quad k = -3
\]
In simpler words, the values of \( k \) are 3 and -3! The solution set is \( \{ 3, -3 \} \).
make this smaller
1 answer
To find \( k \) in the equation \( 7 + 2k^2 = 25 \):
Start with the equation: \[ 7 + 2k^2 = 25 \]
Subtract 7 from both sides: \[ 2k^2 = 18 \]
Divide by 2: \[ k^2 = 9 \]
Take the square root: \[ k = \pm 3 \]
Thus, the values of \( k \) are \( 3 \) and \( -3 \). The solution set is \( { 3, -3 } \).
