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

Solution for (x-2)(x+8)=1 equation:

Simplifying
(x + -2)(x + 8) = 1

Reorder the terms:
(-2 + x)(x + 8) = 1

Reorder the terms:
(-2 + x)(8 + x) = 1

Multiply (-2 + x) * (8 + x)
(-2(8 + x) + x(8 + x)) = 1
((8 * -2 + x * -2) + x(8 + x)) = 1
((-16 + -2x) + x(8 + x)) = 1
(-16 + -2x + (8 * x + x * x)) = 1
(-16 + -2x + (8x + x2)) = 1

Combine like terms: -2x + 8x = 6x
(-16 + 6x + x2) = 1

Solving
-16 + 6x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-16 + -1 + 6x + x2 = 1 + -1

Combine like terms: -16 + -1 = -17
-17 + 6x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-17 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 6x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 6x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 6x + x2 = 0 + 17
6x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
6x + x2 = 17

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 17 + 9

Reorder the terms:
9 + 6x + x2 = 17 + 9

Combine like terms: 17 + 9 = 26
9 + 6x + x2 = 26

Factor a perfect square on the left side:
(x + 3)(x + 3) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + 3) equal to 5.099019514 and -5.099019514.

Subproblem 1
x + 3 = 5.099019514

Simplifying
x + 3 = 5.099019514

Reorder the terms:
3 + x = 5.099019514

Solving
3 + x = 5.099019514

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 5.099019514 + -3

Combine like terms: 3 + -3 = 0
0 + x = 5.099019514 + -3
x = 5.099019514 + -3

Combine like terms: 5.099019514 + -3 = 2.099019514
x = 2.099019514

Simplifying
x = 2.099019514

Subproblem 2
x + 3 = -5.099019514

Simplifying
x + 3 = -5.099019514

Reorder the terms:
3 + x = -5.099019514

Solving
3 + x = -5.099019514

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -5.099019514 + -3

Combine like terms: 3 + -3 = 0
0 + x = -5.099019514 + -3
x = -5.099019514 + -3

Combine like terms: -5.099019514 + -3 = -8.099019514
x = -8.099019514

Simplifying
x = -8.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.099019514, -8.099019514}