(x+2)(x+20)=1

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Solution for (x+2)(x+20)=1 equation: 


Simplifying
(x + 2)(x + 20) = 1

Reorder the terms:
(2 + x)(x + 20) = 1

Reorder the terms:
(2 + x)(20 + x) = 1

Multiply (2 + x) * (20 + x)
(2(20 + x) + x(20 + x)) = 1
((20 * 2 + x * 2) + x(20 + x)) = 1
((40 + 2x) + x(20 + x)) = 1
(40 + 2x + (20 * x + x * x)) = 1
(40 + 2x + (20x + x2)) = 1

Combine like terms: 2x + 20x = 22x
(40 + 22x + x2) = 1

Solving
40 + 22x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
40 + -1 + 22x + x2 = 1 + -1

Combine like terms: 40 + -1 = 39
39 + 22x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
39 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 22x + -39 + x2 = 0 + -39

Reorder the terms:
39 + -39 + 22x + x2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 22x + x2 = 0 + -39
22x + x2 = 0 + -39

Combine like terms: 0 + -39 = -39
22x + x2 = -39

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -39 + 121

Reorder the terms:
121 + 22x + x2 = -39 + 121

Combine like terms: -39 + 121 = 82
121 + 22x + x2 = 82

Factor a perfect square on the left side:
(x + 11)(x + 11) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 11) equal to 9.055385138 and -9.055385138.


Subproblem 1
x + 11 = 9.055385138

Simplifying
x + 11 = 9.055385138

Reorder the terms:
11 + x = 9.055385138

Solving
11 + x = 9.055385138

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 9.055385138 + -11

Combine like terms: 11 + -11 = 0
0 + x = 9.055385138 + -11
x = 9.055385138 + -11

Combine like terms: 9.055385138 + -11 = -1.944614862
x = -1.944614862

Simplifying
x = -1.944614862


Subproblem 2
x + 11 = -9.055385138

Simplifying
x + 11 = -9.055385138

Reorder the terms:
11 + x = -9.055385138

Solving
11 + x = -9.055385138

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -9.055385138 + -11

Combine like terms: 11 + -11 = 0
0 + x = -9.055385138 + -11
x = -9.055385138 + -11

Combine like terms: -9.055385138 + -11 = -20.055385138
x = -20.055385138

Simplifying
x = -20.055385138


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.944614862, -20.055385138}

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