To solve the equation:
[tex]\[ -\frac{1}{2} n^2 + 18 = 0 \][/tex]
1. First, we want to eliminate the fraction. Multiply every term in the equation by -2 to get:
[tex]\[ n^2 - 36 = 0 \][/tex]
2. Then, solve for [tex]\( n^2 \)[/tex]:
[tex]\[ n^2 = 36 \][/tex]
3. Next, take the square root of both sides to find [tex]\( n \)[/tex]:
[tex]\[ n = \pm \sqrt{36} \][/tex]
4. Since the square root of 36 is 6, we have:
[tex]\[ n = \pm 6 \][/tex]
Therefore, the solutions are:
[tex]\[ n = \pm 6 \][/tex]
So, the values for [tex]\( n \)[/tex] are 6 and -6.
