Rewrite the following quadratic equation in standard form and then solve by factoring out the GCF: 6x2=22x

Question

.(1 point)
The smaller solution is x=
, and the larger solution is x=
.
Remaining Attempts : 3

Answer 1

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

Subtract \( 22x \) from both sides:

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

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

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

Now we can set each factor equal to zero:

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

From the first equation \( 2x = 0 \):

\[ x = 0 \]

From the second equation \( 3x - 11 = 0 \):

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

So, the solutions are:

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

Final answers:

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