(x-1)(x+1)=(x-2)+144

Solution for (x-1)(x+1)=(x-2)+144 equation:

Simplifying
(x + -1)(x + 1) = (x + -2) + 144

Reorder the terms:
(-1 + x)(x + 1) = (x + -2) + 144

Reorder the terms:
(-1 + x)(1 + x) = (x + -2) + 144

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x)) = (x + -2) + 144
((1 * -1 + x * -1) + x(1 + x)) = (x + -2) + 144
((-1 + -1x) + x(1 + x)) = (x + -2) + 144
(-1 + -1x + (1 * x + x * x)) = (x + -2) + 144
(-1 + -1x + (1x + x2)) = (x + -2) + 144

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) = (x + -2) + 144
(-1 + x2) = (x + -2) + 144

Reorder the terms:
-1 + x2 = (-2 + x) + 144

Remove parenthesis around (-2 + x)
-1 + x2 = -2 + x + 144

Reorder the terms:
-1 + x2 = -2 + 144 + x

Combine like terms: -2 + 144 = 142
-1 + x2 = 142 + x

Solving
-1 + x2 = 142 + x

Solving for variable 'x'.

Reorder the terms:
-1 + -142 + -1x + x2 = 142 + x + -142 + -1x

Combine like terms: -1 + -142 = -143
-143 + -1x + x2 = 142 + x + -142 + -1x

Reorder the terms:
-143 + -1x + x2 = 142 + -142 + x + -1x

Combine like terms: 142 + -142 = 0
-143 + -1x + x2 = 0 + x + -1x
-143 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-143 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '143' to each side of the equation.
-143 + -1x + 143 + x2 = 0 + 143

Reorder the terms:
-143 + 143 + -1x + x2 = 0 + 143

Combine like terms: -143 + 143 = 0
0 + -1x + x2 = 0 + 143
-1x + x2 = 0 + 143

Combine like terms: 0 + 143 = 143
-1x + x2 = 143

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 143 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 143 + 0.25

Combine like terms: 143 + 0.25 = 143.25
0.25 + -1x + x2 = 143.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 143.25

Calculate the square root of the right side: 11.968709204

Break this problem into two subproblems by setting 
(x + -0.5) equal to 11.968709204 and -11.968709204.

Subproblem 1
x + -0.5 = 11.968709204

Simplifying
x + -0.5 = 11.968709204

Reorder the terms:
-0.5 + x = 11.968709204

Solving
-0.5 + x = 11.968709204

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 11.968709204 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 11.968709204 + 0.5
x = 11.968709204 + 0.5

Combine like terms: 11.968709204 + 0.5 = 12.468709204
x = 12.468709204

Simplifying
x = 12.468709204

Subproblem 2
x + -0.5 = -11.968709204

Simplifying
x + -0.5 = -11.968709204

Reorder the terms:
-0.5 + x = -11.968709204

Solving
-0.5 + x = -11.968709204

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -11.968709204 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -11.968709204 + 0.5
x = -11.968709204 + 0.5

Combine like terms: -11.968709204 + 0.5 = -11.468709204
x = -11.468709204

Simplifying
x = -11.468709204

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.468709204, -11.468709204}