To rewrite the given 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 factor out the greatest common factor (GCF), which is 2x:
\[ 2x(3x - 11) = 0 \]
Now we can solve for \(x\) by setting each factor equal to zero:
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From \(2x = 0\): \[ x = 0 \]
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From \(3x - 11 = 0\): \[ 3x = 11 \implies x = \frac{11}{3} \]
Now we have both solutions. The smaller solution is:
\[ x = 0 \]
And the larger solution is:
\[ x = \frac{11}{3} \]
Thus, the answers are:
- The smaller solution is \(x = 0\)
- The larger solution is \(x = \frac{11}{3}\)