To solve the equation [tex]\(-\frac{1}{2} n^2 + 18 = 0\)[/tex], follow these steps:
1. Rewrite the equation in standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex]:
[tex]\[
-\frac{1}{2} n^2 + 18 = 0
\][/tex]
2. Move the constant term to the other side of the equation by subtracting 18 from both sides:
[tex]\[
-\frac{1}{2} n^2 = -18
\][/tex]
3. Multiply both sides by [tex]\(-2\)[/tex] to eliminate the fraction:
[tex]\[
n^2 = 36
\][/tex]
4. Take the square root of both sides to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \pm \sqrt{36}
\][/tex]
5. Simplify the square root:
[tex]\[
n = \pm 6
\][/tex]
So, the solution of the equation is:
[tex]\[
n = \pm 6
\][/tex]
