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

Question

The solution set is x={−313,159}
.
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={−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={−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 equal to zero and solve for \(x\).

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

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

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

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

Answer 2

um try again?

Answer 3

Let's go through the solution to the equation \((13x + 3)(9x - 14) = 0\) step by step again.

1. Set each factor equal to zero:

   For the first factor: \[ 13x + 3 = 0 \] Subtract \(3\) from both sides: \[ 13x = -3 \] Divide by \(13\): \[ x = -\frac{3}{13} \]

   For the second factor: \[ 9x - 14 = 0 \] Add \(14\) to both sides: \[ 9x = 14 \] Divide by \(9\): \[ x = \frac{14}{9} \]

So the solutions are: \[ x = -\frac{3}{13} \quad \text{and} \quad x = \frac{14}{9} \]

Now combining both solutions, we get the solution set: \[ x = \left{ -\frac{3}{13}, \frac{14}{9} \right} \]

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