-(2x-1)(x-3)%3D(x%2B5)(x-1).jpeg "(v) (2x-1)(x-3)=(x+5)(x-1)")
Solving the Equation: (2x-1)(x-3) = (x+5)(x-1)
This article will guide you through the process of solving the equation (2x-1)(x-3) = (x+5)(x-1).
Step 1: Expand both sides of the equation
We start by expanding both sides of the equation using the distributive property (or FOIL method).
- Left side: (2x-1)(x-3) = 2x(x-3) - 1(x-3) = 2x² - 6x - x + 3 = 2x² - 7x + 3
- Right side: (x+5)(x-1) = x(x-1) + 5(x-1) = x² - x + 5x - 5 = x² + 4x - 5
Now our equation becomes: 2x² - 7x + 3 = x² + 4x - 5
Step 2: Move all terms to one side
To solve for x, we need to set the equation to zero. We can achieve this by subtracting the terms on the right side from both sides:
2x² - 7x + 3 - (x² + 4x - 5) = 0
Simplifying, we get: x² - 11x + 8 = 0
Step 3: Solve the quadratic equation
We now have a quadratic equation in the form of ax² + bx + c = 0. There are a few ways to solve this:
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Factoring: In this case, factoring might be a bit tricky.
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Quadratic formula: The quadratic formula is a reliable method to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
In our equation, a = 1, b = -11, and c = 8. Plugging these values into the formula, we get:
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
Conclusion
We have successfully solved the equation (2x-1)(x-3) = (x+5)(x-1). The solutions are x = (11 + √89) / 2 and x = (11 - √89) / 2. You can verify these solutions by plugging them back into the original equation.