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What is the solution of this equation?
[tex]\[
-\frac{1}{2} n^2 + 18 = 0
\][/tex]
[tex]\[
n = \pm \square
\][/tex]



Answer :

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]