(x%2B2)%3D(2x-3)(x%2B4).jpeg "(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