Solve the equation x^2 = 36/169

A: { -6/13}

B: { 6/13}

C: There are no real solutions.

D: { -6/13, 6/13}

1 answer

To solve the equation \( x^2 = \frac{36}{169} \), we can take the square root of both sides.

The square root of both sides gives us:

\[ x = \pm \sqrt{\frac{36}{169}} \]

Since \( \sqrt{\frac{36}{169}} = \frac{\sqrt{36}}{\sqrt{169}} = \frac{6}{13} \), we have:

\[ x = \pm \frac{6}{13} \]

This results in two possible solutions:

\[ x = \frac{6}{13} \quad \text{and} \quad x = -\frac{6}{13} \]

Thus, the complete solution set is:

\[ { -\frac{6}{13}, \frac{6}{13} } \]

So the correct answer is:

D: \( { -\frac{6}{13}, \frac{6}{13} } \)