Let's solve the equation step-by-step:
[tex]\[ -\frac{1}{2} n^2 + 18 = 0 \][/tex]
First, we want to isolate the [tex]\( n^2 \)[/tex] term. To do this, subtract 18 from both sides of the equation:
[tex]\[ -\frac{1}{2} n^2 = -18 \][/tex]
Next, to eliminate the fraction, multiply both sides of the equation by [tex]\(-2\)[/tex]:
[tex]\[ n^2 = 36 \][/tex]
Now, take the square root of both sides to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \pm \sqrt{36} \][/tex]
Thus, we find two solutions:
[tex]\[ n = 6 \quad \text{and} \quad n = -6 \][/tex]
So, the solutions to the equation [tex]\( -\frac{1}{2} n^2 + 18 = 0 \)[/tex] are:
[tex]\[ 6 \quad \text{and} \quad -6 \][/tex]
Therefore, the solutions are [tex]\( n = 6 \)[/tex] and [tex]\( n = -6 \)[/tex].
