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

Question

.(1 point)
The smaller solution is x=
, and the larger solution is x=
.

Answer 1

To solve the quadratic equation \(2x^2 - 14x = 0\) by factoring out the greatest common factor (GCF), we first identify the GCF in the equation.

The GCF of \(2x^2\) and \(-14x\) is \(2x\).

Now, we factor \(2x\) out of the equation:

\[ 2x(x - 7) = 0 \]

Now, we can set each factor equal to zero:

1. \(2x = 0\)
2. \(x - 7 = 0\)

For the first equation \(2x = 0\):

\[ x = 0 \]

For the second equation \(x - 7 = 0\):

\[ x = 7 \]

Thus, the solutions to the equation are \(x = 0\) and \(x = 7\).

The smaller solution is \(x = 0\), and the larger solution is \(x = 7\).