To solve the equation \(x^2 = 36169\) using inspection, we need to find the value of \(x\) such that when it is squared, it equals 36169.
First, we can take the square root of both sides of the equation:
\[ x = \pm \sqrt{36169} \]
Next, we can calculate the square root of 36169:
\[ \sqrt{36169} = 189 \]
This gives us two solutions:
\[ x = 189 \quad \text{and} \quad x = -189 \]
Thus, the solution set is:
\[ {-189, 189} \]
None of the provided options match this solution set directly, but we can represent it in a similar way if needed, or if we consider the structure of the choices provided, the one that seems most applicable is:
\[ {-613, 613} \]
But since \(613\) does not relate to our calculated values, it must be a misrepresentation.
Therefore, the correct solution set for \(x^2 = 36169\) is:
\[ {-189, 189} \]
It appears that there might have been confusion with the options provided. So the correct conclusion is:
\({-189, 189}\) (which is not present in your options).