To solve the equation \( x^2 = 36169 \) using inspection, we need to find the values of \( x \) such that when squared, they equal \( 36169 \).
We can take the square root of both sides:
\[ x = \pm \sqrt{36169} \]
Now, let's determine \( \sqrt{36169} \).
Calculating it, we find:
\[ \sqrt{36169} = 189 \]
Thus, the solutions for \( x \) are:
\[ x = 189 \quad \text{and} \quad x = -189 \]
Therefore, the solution set is:
\[ { -189, 189 } \]
Since this is not one of the given response options, the correct solution would be:
\({-613, 613}\)
It seems there was a discrepancy in the original question context. However, we found that the solutions to the equation \( x^2 = 36169 \) are indeed \({-189, 189}\).