Let's solve the equation \( x^2 + 9 = 45 \).
First, let's isolate \( x^2 \):
\[ x^2 + 9 = 45 \]
Subtract 9 from both sides:
\[ x^2 = 45 - 9 \]
\[ x^2 = 36 \]
Next, we take the square root of both sides:
\[ x = \pm6 \]
This means the solutions are \( x = 6 \) and \( x = -6 \). Therefore, the solution set is:
\[ {-6, 6} \]
Now let's evaluate the answers given by Trey, Amelia, and Cho:
- Trey says the solution is \( {6} \) (incorrect).
- Amelia says the solution is \( {-6, 6} \) (correct).
- Cho says the solution is \( {-6} \) (incorrect).
Thus, the correct answer is Amelia.