To solve the equation \( x^2 + 9 = 45 \), we first isolate \( x^2 \):
\[ x^2 + 9 = 45 \]
Subtract 9 from both sides:
\[ x^2 = 45 - 9 \] \[ x^2 = 36 \]
Next, we take the square root of both sides. Remember that when we take the square root, we consider both the positive and negative roots:
\[ x = \pm \sqrt{36} \] \[ x = \pm 6 \]
This gives us the solutions \( x = 6 \) and \( x = -6 \). Therefore, the solution set is:
\[ {-6, 6} \]
Now let's compare the responses:
- Trey says the solution is \( {6} \) (not correct, as it misses the negative solution).
- Amelia says the solution is \( {-6, 6} \) (correct).
- Cho says the solution is \( {-6} \) (not correct, as it misses the positive solution).
The person who has found the correct solution set is Amelia.