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=0 and x=421 . The solutions are x equals 0 and x equals Start Fraction 4 over 21 End Fraction . 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 .

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=0 and x=421 . The solutions are x equals 0 and x equals Start Fraction 4 over 21 End Fraction . 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 .

Answer 1

To solve the quadratic equation 84x^2 + 16x = 0 by factoring, we can first find the greatest common factor (GCF) between the terms 84x^2 and 16x, which is 4x. By factoring out 4x, we get:

(4x)(21x + 4) = 0

Now, we can set each factor equal to zero and solve for x:

4x = 0 or 21x + 4 = 0

For 4x = 0, we divide both sides by 4 to isolate x:

x = 0

For 21x + 4 = 0, we subtract 4 from both sides and then divide by 21 to solve for x:

21x + 4 - 4 = 0 - 4
21x = -4
x = -4/21

Therefore, the solutions to the quadratic equation 84x^2 + 16x = 0, by factoring out the GCF, are x = 0 and x = -4/21. The correct answer is:

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

Answer 2

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

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

Factoring out the GCF, we get:
4x(21x + 4) = 0

Now, we set each factor equal to zero and solve for x:

4x = 0 => x = 0

21x + 4 = 0 => 21x = -4 => x = -4/21

Therefore, the solutions are:
x = 0 and x = -4/21

Answer 3

To solve the quadratic equation 84x^2 + 16x = 0 by factoring out the GCF, we need to find the greatest common factor (GCF) of the terms 84x^2 and 16x.

Step 1: Find the GCF of the coefficients (numbers) 84 and 16. The GCF of 84 and 16 is 4.

Step 2: Find the GCF of the variables (x) raised to the highest power. Both terms have x raised to the power of 1, so the GCF is x.

Step 3: Combine the GCF of the coefficients and the GCF of the variables. In this case, it is 4x.

Step 4: Divide both sides of the equation by the common factor 4x to isolate x.

(84x^2 + 16x) / (4x) = 0 / (4x)
21x + 4 = 0

Step 5: Solve the resulting linear equation by isolating x.

21x = -4
x = -4 / 21

Therefore, the solutions to the quadratic equation 84x^2 + 16x = 0, obtained by factoring out the GCF, are x = 0 and x = -4/21.