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