(x-1)(x+2)=(2x-3)(x+4)

2 min read Jun 17, 2024
(x-1)(x+2)=(2x-3)(x+4)

Solving the Equation: (x-1)(x+2) = (2x-3)(x+4)

This equation involves expanding brackets and rearranging terms to solve for x. Let's break down the steps:

1. Expand the brackets:

  • On the left side: (x-1)(x+2) = x² + 2x - x - 2 = x² + x - 2
  • On the right side: (2x-3)(x+4) = 2x² + 8x - 3x - 12 = 2x² + 5x - 12

Now, the equation becomes: x² + x - 2 = 2x² + 5x - 12

2. Rearrange the equation:

To solve for x, we need to have all terms on one side and set the equation to zero. Let's move all terms to the right side:

  • 0 = 2x² + 5x - 12 - x² - x + 2
  • 0 = x² + 4x - 10

3. Solve for x:

Now, we have a quadratic equation in the form ax² + bx + c = 0. We can solve for x using the quadratic formula:

  • x = (-b ± √(b² - 4ac)) / 2a

In our equation, a = 1, b = 4, and c = -10. Substituting these values into the formula, we get:

  • x = (-4 ± √(4² - 4 * 1 * -10)) / (2 * 1)
  • x = (-4 ± √(56)) / 2
  • x = (-4 ± 2√14) / 2
  • x = -2 ± √14

Therefore, the solutions to the equation are:

  • x = -2 + √14
  • x = -2 - √14