Question

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

The solutions are x=0
and x=4
The solutions are x is equal to 0 and x is equal to 4

The solutions are x=−4
and x=−421
The solutions are x is equal to negative 4 and x is equal to negative 4 over 21

The solutions are x=−421
and x=0

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.

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

Next, we factor out \( 4x \) from the equation:

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

Now, we set each factor to zero:

1. \( 4x = 0 \)
- This gives us \( x = 0 \).

2. \( 21x + 4 = 0 \)
- To solve for \( x \), we rearrange the equation:
\[
21x = -4 \quad \Rightarrow \quad x = -\frac{4}{21}
\]

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

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

Thus, the correct response is:

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