Solving the Equation x = 3x^2: A Simple Guide

To solve the equation x = 3x^2, follow these steps:

1. Rearrange the equation: Subtract x from both sides to get: 0 = 3x^2 - x

2. Factor out a common factor: Factor out 'x' from the right side: 0 = x(3x - 1)

3. Set each factor to zero: For the equation to equal zero, either x = 0 or 3x - 1 = 0

4. Solve for x:

   • If x = 0, we have one solution.
   • If 3x - 1 = 0, then 3x = 1 and x = 1/3. This is our second solution.

Therefore, the solutions to the equation x = 3x^2 are x = 0 and x = 1/3.