Solving the Equation x = 3x^2

Solving the Equation x = 3x^2

This equation is a quadratic equation because it contains a term with x raised to the power of 2. To solve for x, we need to follow these steps:

1. Rearrange the equation: Subtract x from both sides to get all terms on one side. This gives us:

   0 = 3x^2 - x

2. Factor out x: Notice that both terms on the right side have x in common. We can 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 the factors must be zero. So, we have two possibilities:

   • x = 0
   • 3x - 1 = 0

4. Solve 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
• x = 1/3