Solve the quadratic equation 84x2+16x=0 by factoring out the GCF.(1 point)

Question

Responses

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.
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=4/21.

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 terms in the equation.

The GCF of \( 84x^2 \) and \( 16x \) is \( 4x \).

Now, we can factor the equation:

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

Setting each factor equal to zero gives us:

1. \( 4x = 0 \) which simplifies to \( x = 0 \).
2. \( 21x + 4 = 0 \) which simplifies to \( 21x = -4 \) and thus \( x = -\frac{4}{21} \).

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

So the correct response is:

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