To determine how many solutions exist for the equation 3x² – 22x = 0, we start by factoring the equation. First, we can factor out an x from the expression:
3x(x – rac{22}{3}) = 0
From this factored form, we can set each factor equal to zero:
1. 3x = 0
2. x – rac{22}{3} = 0
Solving the first equation gives:
x = 0
For the second equation, solving gives:
x = rac{22}{3}
Thus, we find two solutions: x = 0 and x = rac{22}{3}. This means the equation 3x² – 22x = 0 has two distinct solutions.