Solving the Equation x = 3x²: A Step-by-Step Guide

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

This guide will walk you through the process of solving the quadratic equation x = 3xﾲ.

1. Rearrange the equation: Subtract 'x' from both sides to get all terms on one side: 0 = 3xﾲ - x

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

3. Set each factor equal 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: 3x = 1 Divide both sides by 3: x = 1/3

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