To solve the equation \( x^2 + 9 = 45 \), we can first isolate the \( x^2 \) term:
\[ x^2 + 9 - 9 = 45 - 9 \] \[ x^2 = 36 \]
Next, we take the square root of both sides:
\[ x = \sqrt{36} \quad \text{or} \quad x = -\sqrt{36} \] \[ x = 6 \quad \text{or} \quad x = -6 \]
Thus, the solutions are \( x = 6 \) and \( x = -6 \).
The solution set can be expressed in set notation as:
\[ {-6, 6} \]
Therefore, the correct choice is:
B. {-6, 6}
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