To solve the equation [tex]\(-3n^2 + 147 = 0\)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
-3n^2 + 147 = 0
\][/tex]
2. Move the constant term [tex]\(147\)[/tex] to the other side of the equation by subtracting [tex]\(147\)[/tex] from both sides:
[tex]\[
-3n^2 = -147
\][/tex]
3. Divide both sides of the equation by [tex]\(-3\)[/tex] to isolate [tex]\(n^2\)[/tex]:
[tex]\[
n^2 = 49
\][/tex]
4. Take the square root of both sides to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \pm \sqrt{49}
\][/tex]
5. Simplify the square root:
[tex]\[
n = \pm 7
\][/tex]
Thus, the solutions to the equation are:
[tex]\[
n = \pm 7
\][/tex]
