(2x-1)(x-3)=(x+5)(x-1) Answer

2 min read Jun 16, 2024

Solving the Equation: (2x-1)(x-3) = (x+5)(x-1)

This equation is a quadratic equation in disguise. To solve it, we need to expand the products, simplify, and then solve for x. Let's break it down step by step:

1. Expanding the Products:

On the left-hand side: (2x-1)(x-3) = 2x² - 6x - x + 3 = 2x² - 7x + 3
On the right-hand side: (x+5)(x-1) = x² - x + 5x - 5 = x² + 4x - 5

2. Setting the Equation:

Now we have: 2x² - 7x + 3 = x² + 4x - 5

3. Simplifying the Equation:

Subtract x² from both sides: x² - 7x + 3 = 4x - 5
Subtract 4x from both sides: x² - 11x + 3 = -5
Add 5 to both sides: x² - 11x + 8 = 0

4. Solving the Quadratic Equation:

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

x = (-b ± √(b² - 4ac)) / 2a

In our equation, a = 1, b = -11, c = 8. Let's plug these values into the quadratic formula:

x = (11 ± √((-11)² - 4 * 1 * 8)) / (2 * 1)
x = (11 ± √(89)) / 2

Therefore, the solutions to the equation are:

x = (11 + √89) / 2
x = (11 - √89) / 2

These are the exact solutions. You can approximate them to decimal values if needed.