Question


Question
Rewrite the following quadratic equation in standard form and then solve by factoring out the GCF: 6x2=22x.(1 point)
The smaller solution is x=
, and the larger solution is x=
.

Answers

GPT-4o mini
To rewrite the quadratic equation \( 6x^2 = 22x \) in standard form, 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 of the equation. The GCF of 6 and 22 is 2, so we can factor out \( 2x \):

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

Now, we set each factor equal to zero:

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

For the first factor:

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

For the second factor:

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

Now we have the solutions:

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

So, we can state:

The smaller solution is \( \boxed{0} \), and the larger solution is \( \boxed{\frac{11}{3}} \).

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