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To solve the equation \( x^2 + 9 = 45 \):
1. Subtract 9 from both sides:
\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]
2. Take the square root of both sides, noting that this includes both the positive and negative roots:
\[
x = 6 \quad \text{or} \quad x = -6
\]
Thus, the solution set is \( \{-6, 6\} \).
Amelia is correct.