Question

Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x^2−14x=0
.(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 of the terms on the left side.

The GCF of \(2x^2\) and \(-14x\) is \(2x\). Now we factor \(2x\) out of the equation:

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

Next, we set each factor equal to zero:

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

For the first equation:

\[
2x = 0 \implies x = 0
\]

For the second equation:

\[
x - 7 = 0 \implies x = 7
\]

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

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

Final answers:
- Smaller solution: \(x = 0\)
- Larger solution: \(x = 7\)