Solve the quadratic equation 84x^2+16x=0

Question

by factoring out the GCF.(1 point)
Responses

The solutions are x=0
and x=4/21
.
The solutions are x equals 0 and x equals Start Fraction 4 over 21 End Fraction .

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=−4/21
and x=0
.

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 \( 4x \). We can factor this out:

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

Now we set each factor equal to zero to find the solutions:

1. \( 4x = 0 \)

   • Dividing both sides by 4 gives: \( x = 0 \)

2. \( 21x + 4 = 0 \)

   • Subtracting 4 from both sides gives: \( 21x = -4 \)
   • Dividing by 21 gives: \( x = -\frac{4}{21} \)

Therefore, the solutions are:

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

So, the correct response is:

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