Answer
$x=\pm 3i$
Work Step by Step
Step 1: $x^{2}+9=0$
Step 2: $x^{2}=-9$
Step 3: Using the square root property, $x=\pm\sqrt {-9}$.
Step 4: $x=\pm\sqrt {-1\times9}$
Step 5: $x=\pm\sqrt {-1}\times\sqrt {9}$
Step 6: $x=\pm i\times3$
Step 7: $x=\pm 3i$