Chapter 8 - Radical Functions - 8.5 Complex Numbers - 8.5 Exercises - Page 663: 69

$x=\pm 3i$

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: $x=\pm 3i$