To solve the equation \( x^2 = 36169 \) using inspection, we find the square root of \( 36169 \).
Calculating the square root, we see:
\[ \sqrt{36169} = 189 \]
Thus, the solutions to the equation \( x^2 = 36169 \) are:
\[ x = 189 \quad \text{and} \quad x = -189 \]
So the solution set is:
\[ { -189, 189 } \]
Now looking through your given options, none directly mention { -189, 189 }, so it appears that the options listed are not applicable to this particular equation (perhaps there was a transcription error with the numbers).
Given this, as none of the choices provided accurately reflect the real solutions found, none of the provided responses are correct.
The correct solution set is { -189, 189 }, which is not listed among your options.