Solving Quadratic Equations Using Common Factors Practice

Question

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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=
.
Remaining Attempts : 3
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Answer 1

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

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

Next, factor out the greatest common factor (GCF) from the left side:

The GCF of \(6x^2\) and \(-22x\) is \(2x\), so we factor it out:

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

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

1. \(2x = 0\)

   • Dividing both sides by 2 gives \(x = 0\).

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

   • Add 11 to both sides: \[ 3x = 11 \]
   • Divide by 3: \[ x = \frac{11}{3} \]

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

Final answers:

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