Question

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), follow these steps:

1. **Identify the GCF**: The GCF of the coefficients 84 and 16 is 4.

2. **Factor out the GCF**:
\[
84x^2 + 16x = 4(21x^2 + 4x) = 0
\]

3. **Set each factor to zero**:
\[
4 = 0 \quad \text{(This does not give any solutions)}
\]
\[
21x^2 + 4x = 0
\]

4. **Factor out \(x\)** from \(21x^2 + 4x\):
\[
x(21x + 4) = 0
\]

5. **Set each factor to zero**:
- From \(x = 0\), we get one solution:
\[
x = 0
\]

- From \(21x + 4 = 0\):
\[
21x = -4 \implies x = -\frac{4}{21}
\]

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

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

Given the response options, the correct answer is:

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