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

Question

Responses

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=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=−4 and x=−421.

Answer 1

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

The GCF of \( 84x^2 \) and \( 16x \) is \( 4x \). We can factor that out:

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

Next, we solve for \( x \) by setting each factor equal to zero:

1. \( 4x = 0 \) gives us: \[ x = 0 \]

2. \( 21x + 4 = 0 \) gives us: \[ 21x = -4 \implies x = -\frac{4}{21} \]

Thus, the solutions to the equation \( 84x^2 + 16x = 0 \) are:

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

Among the provided responses, the correct answer is:

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