(2x-1)2=(x+1)2 In Standard Form

2 min read Jun 16, 2024

Solving the Equation (2x-1)² = (x+1)² in Standard Form

This equation involves squaring expressions, so we need to expand them first before simplifying and rearranging into standard form. Let's break down the steps:

1. Expanding the Squares

Left side: (2x - 1)² = (2x - 1)(2x - 1) = 4x² - 2x - 2x + 1 = 4x² - 4x + 1
Right side: (x + 1)² = (x + 1)(x + 1) = x² + x + x + 1 = x² + 2x + 1

2. Combining Like Terms

Now our equation looks like this: 4x² - 4x + 1 = x² + 2x + 1

3. Rearranging to Standard Form

To get the standard form (ax² + bx + c = 0), we need to move all terms to one side:

Subtract x² from both sides: 3x² - 4x + 1 = 2x + 1
Subtract 2x from both sides: 3x² - 6x + 1 = 1
Subtract 1 from both sides: 3x² - 6x = 0

4. Standard Form

The equation 3x² - 6x = 0 is now in standard form (ax² + bx + c = 0) where a = 3, b = -6, and c = 0.

Important Note: While this equation is in standard form, you can further simplify it by factoring out a common factor of 3x: 3x(x - 2) = 0

This factored form allows you to easily find the solutions (roots) of the equation: x = 0 and x = 2.