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To solve the equation \(x^2 + 9 = 45\), we first isolate \(x^2\):
\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]
Next, we take the square root of both sides:
\[
x = \pm \sqrt{36}
\]
\[
x = \pm 6
\]
This means the solution set is \(\{-6, 6\}\).
Among the responses:
- 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**.