To solve the equation \( x^2 = 81 \) by inspection, we can think about what number squared gives us 81.
The two numbers that satisfy this equation are:
- \( 9 \) because \( 9^2 = 81 \)
- \( -9 \) because \( (-9)^2 = 81 \)
Thus, the complete solution set is:
\({ -9, 9 }\)
So the correct response is:
\({-9, 9}\)