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To solve the equation \( x^2 + 9 = 45 \), we first isolate \( x^2 \):
1. Subtract 9 from both sides:
\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]
2. Next, take the square root of both sides:
\[
x = \pm 6
\]
Thus, the solutions to the equation are \( -6 \) and \( 6 \).
Now, examining the options:
- Trey says the solution is {6}. **Incorrect.**
- Amelia says the solution is {−6, 6}. **Correct.**
- Cho says the solution is {−6}. **Incorrect.**
Therefore, Amelia has found the correct solution set.
The answer is:
**Amelia**