Solve the quadratic equation 84x2+16x=0

Question

by factoring out the GCF.(1 point)
Responses

The solutions are x=−4/21 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=−4/21
.
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=4/21.

Answer 1

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

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 factored expression equal to zero:

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

This gives us:

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

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

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

Setting each factor equal to zero gives us the solutions:

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

Thus, the solutions are:

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

Therefore, the correct response is:

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