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 \( 2x \). We can factor this out:

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

Now we have a product equal to zero, which means that we can set each factor equal to zero:

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

Solving the first equation:

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

Solving the second equation:

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

So the solutions to the equation \( 2x^2 - 14x = 0 \) are \( x = 0 \) and \( x = 7 \).

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