To solve the equation [tex]\(-\frac{1}{2} n^2 + 18 = 0\)[/tex], we need to find the values of [tex]\(n\)[/tex] that satisfy this equation. Here are the steps to do so:
1. Isolate the quadratic term: Start by moving the constant term to the other side of the equation.
[tex]\[
-\frac{1}{2} n^2 + 18 = 0 \implies -\frac{1}{2} n^2 = -18
\][/tex]
2. Eliminate the coefficient of the quadratic term: To make the equation simpler, multiply both sides by [tex]\(-2\)[/tex] to get rid of the fraction.
[tex]\[
n^2 = 36
\][/tex]
3. Solve for [tex]\(n\)[/tex]: To find [tex]\(n\)[/tex], take the square root of both sides of the equation.
[tex]\[
n = \pm \sqrt{36}
\][/tex]
4. Calculate the square root: The square root of 36 is 6.
[tex]\[
n = \pm 6
\][/tex]
Therefore, the solutions to the equation are:
[tex]\[
n = \pm 6
\][/tex]
