To solve the equation \( x^2 = \frac{36}{169} \) using inspection, we will take the square root of both sides.
First, we recognize that taking the square root of both sides yields two potential solutions:
\[ x = \sqrt{\frac{36}{169}} \quad \text{or} \quad x = -\sqrt{\frac{36}{169}}. \]
Calculating the square root on the right side, we have:
\[ \sqrt{\frac{36}{169}} = \frac{\sqrt{36}}{\sqrt{169}} = \frac{6}{13}. \]
Thus, the two possible solutions for \( x \) are:
\[ x = \frac{6}{13} \quad \text{and} \quad x = -\frac{6}{13}. \]
This gives us the complete solution set:
\[ { -\frac{6}{13}, \frac{6}{13} }. \]
Now, referring to the options provided, the correct solution set is:
\[ { -\frac{6}{13}, \frac{6}{13} }. \]
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