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=

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 on the left side.

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

Now we can factor out \(2x\):

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

Next, we set each factor to zero:

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

Solving the first equation:

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

Solving the second equation:

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

Thus, the solutions are:

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

Therefore, the answers are:
- The smaller solution is \(x = 0\).
- The larger solution is \(x = 7\).