Solve the quadratic equation 84x^2+16x=0 by factoring out the GCF.(1 point) Responses

Question

A. the solutions are x = 0 and x = 4
B. the solutions are x = 0 and x = 4/21
C. the solutions are x = -4/21 and x = 0
D. the solutions are x = -4 and x = -4/21

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 \( 84x^2 \) and \( 16x \).

The GCF of \( 84 \) and \( 16 \) is \( 4 \). We can factor out \( 4x \) from the equation:

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

Setting this equation to zero gives us two factors to solve for \( x \):

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

From \( 4x = 0 \):

\[ x = 0 \]

From \( 21x + 4 = 0 \):

\[ 21x = -4 \] \[ x = -\frac{4}{21} \]

Thus, the solutions to the equation are:

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

The correct response is:

C. the solutions are x = -4/21 and x = 0