Let's solve the equation [tex]\( 2k^2 = 16^2 \)[/tex] step-by-step.
1. Calculate [tex]\( 16^2 \)[/tex]:
[tex]\[
16^2 = 256
\][/tex]
So, the given equation becomes:
[tex]\[
2k^2 = 256
\][/tex]
2. Isolate [tex]\( k^2 \)[/tex] by dividing both sides of the equation by 2:
[tex]\[
k^2 = \frac{256}{2}
\][/tex]
3. Perform the division:
[tex]\[
k^2 = 128
\][/tex]
4. Solve for [tex]\( k \)[/tex] by taking the square root of both sides:
[tex]\[
k = \pm \sqrt{128}
\][/tex]
5. Evaluate [tex]\( \sqrt{128} \)[/tex]:
[tex]\[
\sqrt{128} \approx 11.313708498984761
\][/tex]
So, there are two possible solutions for [tex]\( k \)[/tex]:
[tex]\[
k \approx 11.313708498984761 \quad \text{and} \quad k \approx -11.313708498984761
\][/tex]
Therefore, the solutions to the equation [tex]\( 2k^2 = 16^2 \)[/tex] are approximately [tex]\( k = 11.313708498984761 \)[/tex] and [tex]\( k = -11.313708498984761 \)[/tex].
