Question

Solve the following quadratic equation by factoring out the greatest common factor (GCF): 6x^2 = 22x.
The smaller solution is x =
The large solution is x =

Answer 1

To solve the quadratic equation \(6x^2 = 22x\), we start by moving all terms to one side of the equation:

\[
6x^2 - 22x = 0
\]

Next, we can factor out the greatest common factor (GCF) from the left side. The GCF of \(6x^2\) and \(-22x\) is \(2x\):

\[
2x(3x - 11) = 0
\]

Now we can set each factor equal to zero:

1. \(2x = 0\)
2. \(3x - 11 = 0\)

For the first equation, solving for \(x\):

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

For the second equation, solving for \(x\):

\[
3x - 11 = 0 \implies 3x = 11 \implies x = \frac{11}{3}
\]

Thus, the solutions to the equation are:

- The smaller solution is \(x = 0\)
- The larger solution is \(x = \frac{11}{3}\)

In summary, the answers are:
- Smaller solution: \(x = 0\)
- Larger solution: \(x = \frac{11}{3}\)