(x-2)^2-(x-3)(x+3)=6

2 min read Jun 17, 2024

Solving the Equation: (x-2)^2 - (x-3)(x+3) = 6

This article will guide you through the steps of solving the equation (x-2)^2 - (x-3)(x+3) = 6.

First, we need to expand the expressions on the left side of the equation.

(x-2)^2 can be expanded using the formula (a-b)^2 = a^2 - 2ab + b^2:
- (x-2)^2 = x^2 - 4x + 4
(x-3)(x+3) is a difference of squares:
- (x-3)(x+3) = x^2 - 9

Now the equation becomes: x^2 - 4x + 4 - (x^2 - 9) = 6

We can simplify the equation by distributing the negative sign and combining like terms:

x^2 - 4x + 4 - x^2 + 9 = 6 -4x + 13 = 6

To isolate the variable 'x', subtract 13 from both sides of the equation:

-4x = -7

Finally, divide both sides of the equation by -4 to solve for 'x':

x = 7/4

Therefore, the solution to the equation (x-2)^2 - (x-3)(x+3) = 6 is x = 7/4.