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 is a step-by-step process to solve it:
1. Start with the given equation:
[tex]\[
-\frac{1}{2} n^2 + 18 = 0
\][/tex]
2. To eliminate the fraction, multiply every term by [tex]\(-2\)[/tex] to simplify:
[tex]\[
n^2 - 36 = 0
\][/tex]
3. Rewrite the equation to isolate the [tex]\( n^2 \)[/tex] term:
[tex]\[
n^2 = 36
\][/tex]
4. Solve for [tex]\( n \)[/tex] by taking the square root of both sides. Remember that the square root of a number can be both positive and negative:
[tex]\[
n = \pm \sqrt{36}
\][/tex]
5. Simplify the square root:
[tex]\[
\sqrt{36} = 6
\][/tex]
6. Therefore, the solutions to the equation are:
[tex]\[
n = \pm 6
\][/tex]
Thus, the solution of the equation is:
[tex]\[
n = \pm 6
\][/tex]
