To solve the equation \( x^2 = 81 \) using inspection, we can look for values of \( x \) that, when squared, equal 81.
- The square root of 81 is 9.
- Therefore, \( x \) can be 9 or -9, since both \( 9^2 = 81 \) and \( (-9)^2 = 81 \).
Hence, the complete solution set is \( {-9, 9} \).
The correct answer is:
C. {-9, 9}