Question

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

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 in the equation.

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

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

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

Next, we set each factor equal to zero:

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

Solving these equations gives us:

1. From \(2x = 0\):
\[
x = 0
\]

2. From \(x - 7 = 0\):
\[
x = 7
\]

Thus, the solutions to the equation \(2x^2 - 14x = 0\) are:

\[
\boxed{0} \quad \text{and} \quad \boxed{7}
\]