#### Answer

{$\pm 9i$}

#### Work Step by Step

Step 1: $x^{2}=-81$
Step 2: Using the square root property,
$x=\pm\sqrt {-81}$
Step 3: $x=\pm\sqrt {-1\times81}$
Step 4: Using the product rule for radicals,
$x=\pm\sqrt {-1}\times\sqrt {81}$
Step 5: Since $i=\sqrt {-1}$,
$x=\pm i\times\sqrt {81}$
Step 6: $x=\pm i\times9$
Step 7: $x=\pm 9i$
Therefore, the solution set is {$\pm 9i$}.