(x-5)^2-6=(x+1)^2

2 min read Jun 17, 2024

Solving the Equation (x-5)^2 - 6 = (x+1)^2

This article will guide you through solving the equation (x-5)^2 - 6 = (x+1)^2. We'll break down each step to make the process clear and understandable.

Expanding the Equation

First, we need to expand the squared terms using the FOIL method (First, Outer, Inner, Last):

(x-5)^2 = (x-5)(x-5) = x^2 - 10x + 25
(x+1)^2 = (x+1)(x+1) = x^2 + 2x + 1

Now our equation looks like this:

x^2 - 10x + 25 - 6 = x^2 + 2x + 1

Simplifying the Equation

Next, let's simplify the equation by combining like terms:

x^2 - 10x + 19 = x^2 + 2x + 1

We can subtract x^2 from both sides, canceling it out:

-10x + 19 = 2x + 1

Isolating the Variable

Now we need to isolate the variable x. Let's move all x terms to one side and constant terms to the other:

Subtract 2x from both sides: -12x + 19 = 1
Subtract 19 from both sides: -12x = -18

Solving for x

Finally, divide both sides by -12 to solve for x:

x = -18 / -12 = 3/2

Solution

Therefore, the solution to the equation (x-5)^2 - 6 = (x+1)^2 is x = 3/2.