To solve the equation [tex]\(-\frac{1}{2} n^2 + 18 = 0\)[/tex], follow these steps:
1. Rearrange the equation to isolate the quadratic term:
[tex]\[
-\frac{1}{2} n^2 + 18 = 0
\][/tex]
[tex]\[
-\frac{1}{2} n^2 = -18
\][/tex]
[tex]\[
n^2 = \frac{36}{1}
\][/tex]
[tex]\[
n^2 = 36
\][/tex]
2. Take the square root of both sides of the equation to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \pm \sqrt{36}
\][/tex]
3. Simplify the square root of 36:
[tex]\[
n = \pm 6
\][/tex]
Thus, the solution to the equation [tex]\(-\frac{1}{2} n^2 + 18 = 0\)[/tex] is [tex]\( n = \pm 6 \)[/tex]. Therefore, the answer is:
[tex]\[
n = \pm 6
\][/tex]
