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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]

Sagot :

GinnyAnswer
To solve the equation [tex]\(-\frac{1}{2} n^2 + 18 = 0\)[/tex], follow these steps:

1. Rearrange the equation to isolate the quadratic term:
[tex]\[ -\frac{1}{2} n^2 + 18 = 0 \][/tex]
[tex]\[ -\frac{1}{2} n^2 = -18 \][/tex]
[tex]\[ n^2 = \frac{36}{1} \][/tex]
[tex]\[ n^2 = 36 \][/tex]

2. Take the square root of both sides of the equation to solve for [tex]\(n\)[/tex]:
[tex]\[ n = \pm \sqrt{36} \][/tex]

3. Simplify the square root of 36:
[tex]\[ n = \pm 6 \][/tex]

Thus, the solution to the equation [tex]\(-\frac{1}{2} n^2 + 18 = 0\)[/tex] is [tex]\( n = \pm 6 \)[/tex]. Therefore, the answer is:

[tex]\[ n = \pm 6 \][/tex]
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