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To solve the equation \( x^2 + 9 = 45 \), we first isolate \( x^2 \):
\[
x^2 + 9 - 9 = 45 - 9
\]
\[
x^2 = 36
\]
Next, we take the square root of both sides:
\[
x = \pm 6
\]
This gives us the solutions \( x = 6 \) and \( x = -6 \). Therefore, the solution set is:
\[
\{-6, 6\}
\]
From the responses:
- Trey says the solution is \{6\} - Incorrect.
- Amelia says the solution is \{-6, 6\} - Correct.
- Cho says the solution is \{-6\} - Incorrect.
So, the correct answer is **Amelia**.