Solve the quadratic equation 84x2+16x=0 by factoring out the GCF.(1 point)

Question

Responses

The solutions are x=0 and x=421.
The solutions are  x equals 0  and  x equals Start Fraction 4 over 21 End Fraction .

The solutions are x=0 and x=4.
The solutions are  x equals 0  and  x equals 4 .

The solutions are x=−421 and x=0.
The solutions are  x equals negative Start Fraction 4 over 21 End Fraction  and  x equals 0 .

The solutions are x=−4 and x=−421.

Answer 1

To solve the quadratic equation \(84x^2 + 16x = 0\) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms in the equation.

The GCF of \(84x^2\) and \(16x\) is \(4x\).

Now we factor \(4x\) out of the equation:

\[ 84x^2 + 16x = 4x(21x + 4) = 0 \]

Next, we set each factor equal to zero:

1. \(4x = 0\)
2. \(21x + 4 = 0\)

From the first factor:

\[ 4x = 0 \implies x = 0 \]

From the second factor:

\[ 21x + 4 = 0 \implies 21x = -4 \implies x = -\frac{4}{21} \]

Thus, the solutions to the equation are:

\[ x = 0 \quad \text{and} \quad x = -\frac{4}{21} \]

Therefore, the correct response is:

The solutions are \(x = 0\) and \(x = -\frac{4}{21}\).