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

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

Now, we can set each factor equal to zero to find the solutions:

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

Solving the first equation:

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

Solving the second equation:

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

Thus, the solutions are:

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

So, we can summarize the solutions as:

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