Use inspection to solve the equation x2=36/169, then select the correct solution set below. If there are no real solutions, select “There are no real solutions.”(1 point) Responses {−613,613} left brace negative Start Fraction 6 over 13 End Fraction comma Start Fraction 6 over 13 End Fraction right brace There are no real solutions. There are no real solutions. {−613} left brace negative Start Fraction 6 over 13 End Fraction right brace {613}
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To solve the equation \( x^2 = \frac{36}{169} \) by inspection, we take the square root of both sides.
First, we simplify the right side:
\[ x = \pm \sqrt{\frac{36}{169}} \]
Next, we can separate the square root:
\[ x = \pm \frac{\sqrt{36}}{\sqrt{169}} = \pm \frac{6}{13} \]
Thus, the solutions are:
\[ x = \frac{6}{13} \quad \text{and} \quad x = -\frac{6}{13} \]
Therefore, the correct solution set is:
\[ {-\frac{6}{13}, \frac{6}{13}} \]
So the final answer is:
\({-\frac{6}{13}, \frac{6}{13}}\)
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