(3x-1)^2-8(x+1)^2=(x+2)(x-2)

2 min read Jun 16, 2024

Solving the Equation: (3x-1)^2 - 8(x+1)^2 = (x+2)(x-2)

This article will guide you through solving the equation (3x-1)^2 - 8(x+1)^2 = (x+2)(x-2). We will use algebraic manipulation to simplify the equation and find the solutions for x.

Expanding the Equation

First, we need to expand the squares and the product on both sides of the equation.

Left side:
- (3x-1)^2 = (3x-1)(3x-1) = 9x^2 - 6x + 1
- 8(x+1)^2 = 8(x+1)(x+1) = 8(x^2 + 2x + 1) = 8x^2 + 16x + 8
Right side:
- (x+2)(x-2) = x^2 - 4

Now, our equation becomes: 9x^2 - 6x + 1 - 8x^2 - 16x - 8 = x^2 - 4

Simplifying the Equation

We can simplify the equation by combining like terms:

x^2 - 22x - 7 = x^2 - 4

Subtracting x^2 from both sides:

-22x - 7 = -4

Adding 7 to both sides:

-22x = 3

Solving for x

Finally, we divide both sides by -22 to isolate x:

x = -3/22

Solution

Therefore, the solution to the equation (3x-1)^2 - 8(x+1)^2 = (x+2)(x-2) is x = -3/22.