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

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

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

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

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

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

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

Solving
-2 + 1x + x2 = 1

Solving for variable 'x'.

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

Combine like terms: -2 + -1 = -3
-3 + 1x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-3 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 1x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1x + x2 = 0 + 3
1x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
1x + x2 = 3

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.
x + 0.25 + x2 = 3 + 0.25

Reorder the terms:
0.25 + x + x2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + x + x2 = 3.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + 0.5 = 1.802775638

Simplifying
x + 0.5 = 1.802775638

Reorder the terms:
0.5 + x = 1.802775638

Solving
0.5 + x = 1.802775638

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 = 1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.802775638 + -0.5
x = 1.802775638 + -0.5

Combine like terms: 1.802775638 + -0.5 = 1.302775638
x = 1.302775638

Simplifying
x = 1.302775638

Subproblem 2
x + 0.5 = -1.802775638

Simplifying
x + 0.5 = -1.802775638

Reorder the terms:
0.5 + x = -1.802775638

Solving
0.5 + x = -1.802775638

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 = -1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.802775638 + -0.5
x = -1.802775638 + -0.5

Combine like terms: -1.802775638 + -0.5 = -2.302775638
x = -2.302775638

Simplifying
x = -2.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.302775638, -2.302775638}