Question

Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x^2 - 14x = 0

The smaller solution is x = _____, and the larger solution is z = ____.

Answer 1

Rewrite the following quadratic equation in standard form and then solve by factoring out the GCF: 6x^2 - 22x.
The smaller solution is x = _____, and the larger solution is x = _____.

Answer 2

To solve the equation by factoring out the greatest common factor (GCF), first we need to find the GCF of 2x^2 and -14x.

The greatest common factor is 2x. We can factor it out:

2x^2 - 14x = 2x(x - 7)

Now we have factored the equation.

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

2x = 0
x = 0

And

x - 7 = 0
x = 7

Therefore, the smaller solution is x = 0, and the larger solution is x = 7.

Answer 3

To rewrite the equation in standard form, we need to make sure the quadratic term has the highest power by rearranging the terms.

The given equation is already in standard form: 6x^2 - 22x.

To solve the equation by factoring out the greatest common factor (GCF), we need to find the GCF of 6x^2 and -22x.

The greatest common factor is 2x. We can factor it out:

6x^2 - 22x = 2x(3x - 11)

Now we have factored the equation.

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

2x = 0
x = 0

And

3x - 11 = 0
3x = 11
x = 11/3

Therefore, the smaller solution is x = 0, and the larger solution is x = 11/3.