Question

Solve the quadratic equation 84x2+16x=0 by factoring out the GCF.(1 point) 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=−4 and x=−421 . The solutions are x equals negative 4 and x equals negative 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=0 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 two terms:

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

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

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

Now we set each factor equal to zero:

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

2. \(21x + 4 = 0\)
Solving for \(x\):
\[
21x = -4
\]
\[
x = -\frac{4}{21}
\]

So the solutions to the equation \(84x^2 + 16x = 0\) are:
\[
x = 0 \quad \text{and} \quad x = -\frac{4}{21}
\]

Thus, the correct option is:
**The solutions are \(x = -\frac{4}{21}\) and \(x = 0\).**