(x-2)(x-4)=8

2 min read Jun 17, 2024

Solving the Quadratic Equation: (x-2)(x-4) = 8

This article will guide you through the process of solving the quadratic equation (x-2)(x-4) = 8. We'll break down the steps and explore the different methods for finding the solutions.

1. Expanding the Equation

First, we need to expand the left side of the equation:

(x-2)(x-4) = 8 x² - 6x + 8 = 8

2. Simplifying the Equation

Next, we simplify the equation by subtracting 8 from both sides:

x² - 6x = 0

3. Factoring the Equation

Now we can factor out an x from the left side:

x(x-6) = 0

4. Solving for x

To find the solutions, we set each factor equal to zero:

x = 0 or x - 6 = 0

Solving for x in the second equation:

x = 6

Solutions

Therefore, the solutions to the equation (x-2)(x-4) = 8 are:

x = 0 and x = 6

Alternative Methods

While factoring is a straightforward method, there are other ways to solve quadratic equations:

Quadratic Formula: This formula can be used to solve any quadratic equation in the form ax² + bx + c = 0.
Completing the Square: This method involves manipulating the equation to create a perfect square trinomial.

You can choose the method that best suits your understanding and preference.

Let me know if you have any more questions about solving quadratic equations!