To solve the quadratic equation \(6x^2 = 22x\), we start by moving all terms to one side of the equation:
\[ 6x^2 - 22x = 0 \]
Next, we can factor out the greatest common factor (GCF) from the left side. The GCF of \(6x^2\) and \(-22x\) is \(2x\):
\[ 2x(3x - 11) = 0 \]
Now we can set each factor equal to zero:
- \(2x = 0\)
- \(3x - 11 = 0\)
For the first equation, solving for \(x\):
\[ 2x = 0 \implies x = 0 \]
For the second equation, solving for \(x\):
\[ 3x - 11 = 0 \implies 3x = 11 \implies x = \frac{11}{3} \]
Thus, the solutions to the equation are:
- The smaller solution is \(x = 0\)
- The larger solution is \(x = \frac{11}{3}\)
In summary, the answers are:
- Smaller solution: \(x = 0\)
- Larger solution: \(x = \frac{11}{3}\)
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