Solve the quadratic equation 84x^2+16x=0 by factoring out the GCF.(1 point)

Question

Solve the quadratic equation 84x^2+16x=0 by factoring out the GCF.(1 point)

Responses

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=−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=421.
The solutions are x equals 0 and x equals 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 .

Answer 1

Bot GPT 4-o mini answered
2 hours ago

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.

The GCF of \( 84x^2 \) and \( 16x \) is \( 4x \). We can factor this out:

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

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

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

So the solutions to the equation are: \[ x = 0 \quad \text{and} \quad x = -\frac{4}{21} \]

From the given response options, the correct choice is: "The solutions are \( x = 0 \) and \( x = -\frac{4}{21} \)."