(x-5)(x+8)-(x-7)(x+7)=3

2 min read Jun 17, 2024

Solving the Equation: (x-5)(x+8)-(x-7)(x+7)=3

This article will guide you through the steps to solve the equation (x-5)(x+8)-(x-7)(x+7)=3.

Expanding the Equation

The first step is to expand the equation by multiplying the terms in the parentheses. We can use the FOIL method (First, Outer, Inner, Last) to do this:

(x-5)(x+8)-(x-7)(x+7)=3

(x-5)(x+8):
- First: x * x = x²
- Outer: x * 8 = 8x
- Inner: -5 * x = -5x
- Last: -5 * 8 = -40
(x-7)(x+7):
- First: x * x = x²
- Outer: x * 7 = 7x
- Inner: -7 * x = -7x
- Last: -7 * 7 = -49

Now, we can rewrite the equation as:

x² + 8x - 5x - 40 - (x² + 7x - 7x - 49) = 3

Simplifying the Equation

Let's simplify the equation by combining like terms:

x² - x² = 0
8x - 5x + 7x - 7x = 3x
-40 + 49 = 9

The equation now becomes:

3x + 9 = 3

Solving for x

To solve for x, we need to isolate it on one side of the equation:

Subtract 9 from both sides:
- 3x + 9 - 9 = 3 - 9
- 3x = -6
Divide both sides by 3:
- 3x / 3 = -6 / 3
- x = -2

Solution

Therefore, the solution to the equation (x-5)(x+8)-(x-7)(x+7)=3 is x = -2.