To solve the given equation [tex]\(-3n^2 + 147 = 0\)[/tex], follow these steps:
1. Move 147 to the other side of the equation:
[tex]\[
-3n^2 = -147
\][/tex]
2. Divide both sides by [tex]\(-3\)[/tex] to isolate [tex]\(n^2\)[/tex]:
[tex]\[
n^2 = 49
\][/tex]
3. Take the square root of both sides to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \pm \sqrt{49}
\][/tex]
4. Simplify the square root of 49:
[tex]\[
\sqrt{49} = 7
\][/tex]
Therefore, the solution is:
[tex]\[
n = \pm 7
\][/tex]
So, the correct answer in the box is:
[tex]\[
n = \pm 7
\][/tex]
