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 need to rearrange it into a standard quadratic form and then apply the appropriate methods.

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

2. Factoring: We can factor out an x from the right side: 0 = x(3x - 1)

3. Zero Product Property: 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. Solving for x: Solving the second equation, we get: * 3x = 1 * x = 1/3

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