solve the following quadratic equation by factoring out the greatest common factor (GCF): 2 x 2−14x=0 .(1 point) The smaller solution is x= , and the larger solution is x= .

Answer 1

To solve the quadratic equation by factoring out the greatest common factor (GCF), we first identify the GCF of the terms.

The two terms in the equation are 2x² and -14x. The GCF of these terms is 2x.

Next, we divide both terms by the GCF (2x) to factor it out:

(2x)(x - 7) = 0

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

2x = 0 → x = 0

x - 7 = 0 → x = 7

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