Certainly! Let's solve the quadratic equation \(-3n^2 + 147 = 0\) step by step.
1. Start with the given equation:
[tex]\[
-3n^2 + 147 = 0
\][/tex]
2. Move 147 to the other side of the equation to isolate the quadratic term:
[tex]\[
-3n^2 = -147
\][/tex]
3. Divide both sides of the equation by -3 to solve for \(n^2\):
[tex]\[
n^2 = \frac{-147}{-3}
\][/tex]
[tex]\[
n^2 = 49
\][/tex]
4. Take the square root of both sides to solve for \(n\):
[tex]\[
n = \pm \sqrt{49}
\][/tex]
5. Calculate the square root of 49:
[tex]\[
n = \pm 7
\][/tex]
Therefore, the solutions are:
[tex]\[
n = \pm 7
\][/tex]
In the box, you should write:
[tex]\[
7
\][/tex]
