(x-8)(x+5)-(x-6)(x+6)=8

3 min read Jun 17, 2024

Solving the Equation: (x-8)(x+5)-(x-6)(x+6)=8

This article will guide you through the steps of solving the equation (x-8)(x+5)-(x-6)(x+6)=8. We'll break it down into manageable steps and explain the reasoning behind each action.

1. Expand the Products

First, we need to expand the products on the left side of the equation. We can use the FOIL method (First, Outer, Inner, Last) to simplify the expressions:

(x-8)(x+5):
- First: x * x = x²
- Outer: x * 5 = 5x
- Inner: -8 * x = -8x
- Last: -8 * 5 = -40
- Combined: x² + 5x - 8x - 40 = x² - 3x - 40
(x-6)(x+6):
- This is a special case of the "difference of squares" pattern: (a - b)(a + b) = a² - b².
- Applying this: (x - 6)(x + 6) = x² - 6² = x² - 36

Now our equation looks like this: x² - 3x - 40 - (x² - 36) = 8

2. Simplify the Equation

Let's simplify the equation by combining like terms:

x² - 3x - 40 - x² + 36 = 8
-3x - 4 = 8

3. Isolate the Variable

We want to isolate the variable "x". To do this, we'll add 4 to both sides of the equation:

-3x - 4 + 4 = 8 + 4
-3x = 12

4. Solve for x

Finally, we'll divide both sides of the equation by -3 to solve for "x":

-3x / -3 = 12 / -3
x = -4

Conclusion

Therefore, the solution to the equation (x-8)(x+5)-(x-6)(x+6)=8 is x = -4.