Question

Rewrite the following quadratic equation in standard form and then solve by factoring out the GCF: 6x^2=22x
.(1 point)
The smaller solution is x=
, and the larger solution is x=

Answer 1

To rewrite the given quadratic equation \(6x^2 = 22x\) in standard form, we first move all terms to one side of the equation:

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

Next, we factor out the greatest common factor (GCF), which is 2x:

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

Now we can solve for \(x\) by setting each factor equal to zero:

1. From \(2x = 0\):
\[
x = 0
\]

2. From \(3x - 11 = 0\):
\[
3x = 11 \implies x = \frac{11}{3}
\]

Now we have both solutions. The smaller solution is:

\[
x = 0
\]

And the larger solution is:

\[
x = \frac{11}{3}
\]

Thus, the answers are:
- The smaller solution is \(x = 0\)
- The larger solution is \(x = \frac{11}{3}\)