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

Question

.(1 point)
Responses

The solution set is x={−313,914}
.
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={−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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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}
.

Answer 1

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

1. \(13x + 3 = 0\)
2. \(9x - 14 = 0\)

Now we solve each equation:

1. For \(13x + 3 = 0\): \[ 13x = -3 \ x = -\frac{3}{13} \]

2. For \(9x - 14 = 0\): \[ 9x = 14 \ x = \frac{14}{9} \]

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

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