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Let's solve the equation \( x^2 + 9 = 45 \) to find the correct solution set.
1. Subtract 9 from both sides:
\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]
2. Take the square root of both sides:
\[
x = \pm 6
\]
Therefore, the solution set is \( \{-6, 6\} \).
Amelia is the one who found the correct solution set.