Solve the factored quadratic equation (13x+3)(9x−14)=0

Question

.(1 point)
Responses

The solution set is x={−313,914}
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The solution set is x equals left brace negative Start Fraction 3 over 13 End Fraction comma Start Fraction 9 over 14 End Fraction right brace .

The solution set is x={−313,159}
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The solution set is x equals left brace negative Start Fraction 3 over 13 End Fraction comma 1 Start Fraction 5 over 9 End Fraction right brace .

The solution set is x={−3,14}
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The solution set is x equals left brace negative 3 comma 14 right brace .

The solution set is x={−133,914}
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Answer 1

To solve the factored quadratic equation \((13x + 3)(9x - 14) = 0\), we can set each factor equal to zero:

1. First factor: \(13x + 3 = 0\) \[ 13x = -3 \quad \Rightarrow \quad x = -\frac{3}{13} \]

2. Second factor: \(9x - 14 = 0\) \[ 9x = 14 \quad \Rightarrow \quad x = \frac{14}{9} \]

Thus, the solution set is: \[ x = \left{-\frac{3}{13}, \frac{14}{9}\right} \]

Therefore, the correct response is: The solution set is \(x = \left{-\frac{3}{13}, \frac{14}{9}\right}\).