To solve the equation \( x^2 = \frac{36}{169} \) using inspection, we can take the square root of both sides.
Starting with the equation: \[ x^2 = \frac{36}{169} \]
Taking the square root of both sides gives: \[ x = \pm \sqrt{\frac{36}{169}} \]
We can simplify that: \[ x = \pm \frac{\sqrt{36}}{\sqrt{169}} = \pm \frac{6}{13} \]
This leads us to the solutions: \[ x = \frac{6}{13} \quad \text{and} \quad x = -\frac{6}{13} \]
Thus, the solution set is: \[ \left{ -\frac{6}{13}, \frac{6}{13} \right} \]
So the correct response is: \[ {−\frac{6}{13}, \frac{6}{13}} \]