Question

Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x2−14x=0
.(1 point)
The smaller solution is x=
, and the larger solution is x=
.
Remaining Attempts : 3

Answer 1

To solve the quadratic equation \( 2x^2 - 14x = 0 \) by factoring out the greatest common factor (GCF), we start by identifying the GCF of the terms 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. \( x - 7 = 0 \)

From the first equation:

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

From the second equation:

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

Thus, the solutions to the equation are:

- The smaller solution is \( x = 0 \)
- The larger solution is \( x = 7 \)

In summary:

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