(x-5)(x-1)=(x-1)(x-2)

2 min read Jun 17, 2024

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

This equation represents a quadratic equation, and our goal is to find the values of 'x' that satisfy the equation. Here's how we can solve it:

1. Expand Both Sides

First, we need to expand both sides of the equation by using the distributive property (also known as FOIL).

Left Side: (x-5)(x-1) = x² - x - 5x + 5 = x² - 6x + 5
Right Side: (x-1)(x-2) = x² - 2x - x + 2 = x² - 3x + 2

Now our equation becomes: x² - 6x + 5 = x² - 3x + 2

2. Simplify the Equation

Since both sides have x², we can subtract x² from both sides, simplifying the equation:

-6x + 5 = -3x + 2

3. Isolate x

To isolate 'x', let's move all the 'x' terms to one side and the constant terms to the other side:

-6x + 3x = 2 - 5

This simplifies to: -3x = -3

4. Solve for x

Finally, divide both sides by -3 to get the value of 'x':

x = (-3) / (-3) = 1

Conclusion

Therefore, the solution to the equation (x-5)(x-1) = (x-1)(x-2) is x = 1. This means that when we substitute 'x' with 1 in the original equation, both sides of the equation will be equal.