How to Solve the Equation x = 3x^2: A Step-by-Step Guide

To solve for x in the equation x = 3x^2, we'll follow these steps:

Rearrange into Standard Quadratic Form: We start by moving all terms to one side of the equation to get it in the standard quadratic form: ax^2 + bx + c = 0.

Subtracting x from both sides, we get:

0 = 3x^2 - x
Identify Coefficients: Now we have a quadratic equation in standard form with a = 3, b = -1, and c = 0.
Apply the Quadratic Formula: To solve for x, we use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a
Substitute Values: Plugging in our coefficients, we have:

x = (1 ± √((-1)^2 - 4 * 3 * 0)) / 2 * 3

x = (1 ± √(1)) / 6
Calculate Solutions: Simplifying the equation, we get two possible solutions:

x = 1/3 or x = 0

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