Solving the Equation x = 3x^2: A Step-by-Step Guide

Solving the Equation x = 3x^2

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

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

2. Factor out x: Notice that both terms on the right side have x in common. Factor out x: 0 = x(3x - 1)

3. Set each factor to zero: For the product of two factors to be zero, at least one of them must be zero. Therefore, we have two possible solutions:

   • x = 0
   • 3x - 1 = 0

4. Solve for x in the second equation: Add 1 to both sides and then divide by 3: 3x = 1 x = 1/3

Solution: The solutions to the equation x = 3x^2 are x = 0 and x = 1/3.