Question

Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x2−14x=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.

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

2. We factor out the GCF \( 2x \):

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

3. Now we can set each factor equal to zero:

\[
2x = 0 \quad \text{or} \quad x - 7 = 0
\]

4. Solving each equation gives:

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

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

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

\[
x = 0 \quad \text{and} \quad x = 7
\]