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 equals 0 and x equals 4 . 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=−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=−421 and x=0.

Answer 1

To solve the quadratic equation \(84x^2 + 16x = 0\) by factoring out the greatest common factor (GCF), let's first identify the GCF of the coefficients 84 and 16.

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

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

Now, we can set the equation inside the parentheses to zero:

\[
21x^2 + 4x = 0
\]

Next, we can factor out an \(x\):

\[
x(21x + 4) = 0
\]

Setting each factor equal to zero gives us the solutions:

1. \(x = 0\)
2. \(21x + 4 = 0\) which leads to \(21x = -4\) or \(x = -\frac{4}{21}\)

Thus, the solutions to the equation are:

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

So, the correct response is:

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