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=

Answer 1

To rewrite the given quadratic equation \( 6x^2 = 22x \) in standard form, we need to move all terms to one side of the equation. Subtracting \( 22x \) from both sides gives:

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

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

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

Now, we set each factor equal to zero.

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

2. \( 3x - 11 = 0 \)
\[
3x = 11 \quad \Rightarrow \quad x = \frac{11}{3}
\]

Thus, we have the solutions:
- Smaller solution: \( x = 0 \)
- Larger solution: \( x = \frac{11}{3} \)

In summary, the smaller solution is \( x = 0 \), and the larger solution is \( x = \frac{11}{3} \).