To solve the equation \( x^2 = 81 \) by inspection, we look for numbers whose squares equal 81.
The square roots of 81 are both 9 and -9, since:
\[ 9^2 = 81 \quad \text{and} \quad (-9)^2 = 81 \]
Therefore, the complete solution set is:
\[ {-9, 9} \]
So the correct response is:
{−9, 9}