To solve the equation \( x^2 = \frac{36}{169} \), we can take the square root of both sides:
\[ x = \pm \sqrt{\frac{36}{169}} \]
Since \( \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \), we have:
\[ x = \pm \frac{\sqrt{36}}{\sqrt{169}} = \pm \frac{6}{13} \]
This gives us two 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 answer is:
\({ -\frac{6}{13}, \frac{6}{13} }\) or \(\left{ -\frac{6}{13}, \frac{6}{13} \right}\) depending on how it is formatted.