To rewrite the quadratic equation \( 6x^2 = 22x \) in standard form, we first need to move all terms to one side of the equation. This gives us:
\[ 6x^2 - 22x = 0 \]
Next, we can factor out the greatest common factor (GCF) from the left-hand side. The GCF of \( 6x^2 \) and \( -22x \) is \( 2x \):
\[ 2x(3x - 11) = 0 \]
Now we set each factor equal to zero:
- \( 2x = 0 \)
- \( 3x - 11 = 0 \)
From the first factor:
\[ 2x = 0 \implies x = 0 \]
From the second factor:
\[ 3x - 11 = 0 \implies 3x = 11 \implies x = \frac{11}{3} \]
Thus, the solutions are:
- The smaller solution is \( x = 0 \).
- The larger solution is \( x = \frac{11}{3} \).