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

Question

.(1 point)
Responses

The solution set is x={−133,914}
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The solution set is x equals left brace negative Start Fraction 13 over 3 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={−313,914}
.

Answer 1

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

1. Set the first factor to zero: \[ 13x + 3 = 0 \] Subtract 3 from both sides: \[ 13x = -3 \] Now, divide by 13: \[ x = -\frac{3}{13} \]

2. Set the second factor to zero: \[ 9x - 14 = 0 \] Add 14 to both sides: \[ 9x = 14 \] Now, divide by 9: \[ x = \frac{14}{9} \]

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

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