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=0
and x=4
.
The solutions are x equals 0 and x equals 4 .

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=421
.

Answer 1

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

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

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

Now we can further factor the expression inside the parentheses:

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

Setting each factor equal to zero gives us the possible solutions:

1. \( 4x = 0 \)
- Dividing both sides by 4 gives \( x = 0 \).

2. \( 21x + 4 = 0 \)
- Subtracting 4 from both sides yields \( 21x = -4 \).
- Dividing both sides by 21 gives \( x = -\frac{4}{21} \).

Thus, the solutions are:

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

The correct response is:

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