Solve for x: x = 3x^2 - Finding the Solutions

Solving for x in the equation x = 3x^2

To solve for x, we need to rearrange the equation into a standard quadratic form (ax^2 + bx + c = 0):

1. Subtract x from both sides: 0 = 3x^2 - x

2. Rearrange the terms: 3x^2 - x = 0

Now we have a quadratic equation. We can solve this using various methods, like factoring, the quadratic formula, or completing the square.

Solution:

One obvious solution is x = 0. This is because if we substitute x = 0 into the original equation, we get:

0 = 3(0)^2

0 = 0

This is true, so x = 0 is a solution.

To find any other solutions, we can factor out an x from the quadratic equation:

x(3x - 1) = 0

For this product to be zero, either x = 0 or (3x - 1) = 0.

Solving (3x - 1) = 0, we get:

3x = 1 x = 1/3

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