(x+4)(x+8)=1

Solution for (x+4)(x+8)=1 equation:

Simplifying
(x + 4)(x + 8) = 1

Reorder the terms:
(4 + x)(x + 8) = 1

Reorder the terms:
(4 + x)(8 + x) = 1

Multiply (4 + x) * (8 + x)
(4(8 + x) + x(8 + x)) = 1
((8 * 4 + x * 4) + x(8 + x)) = 1
((32 + 4x) + x(8 + x)) = 1
(32 + 4x + (8 * x + x * x)) = 1
(32 + 4x + (8x + x2)) = 1

Combine like terms: 4x + 8x = 12x
(32 + 12x + x2) = 1

Solving
32 + 12x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
32 + -1 + 12x + x2 = 1 + -1

Combine like terms: 32 + -1 = 31
31 + 12x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
31 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + 12x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + 12x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 12x + x2 = 0 + -31
12x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
12x + x2 = -31

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -31 + 36

Reorder the terms:
36 + 12x + x2 = -31 + 36

Combine like terms: -31 + 36 = 5
36 + 12x + x2 = 5

Factor a perfect square on the left side:
(x + 6)(x + 6) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 6) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + 6 = 2.236067978

Simplifying
x + 6 = 2.236067978

Reorder the terms:
6 + x = 2.236067978

Solving
6 + x = 2.236067978

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 2.236067978 + -6

Combine like terms: 6 + -6 = 0
0 + x = 2.236067978 + -6
x = 2.236067978 + -6

Combine like terms: 2.236067978 + -6 = -3.763932022
x = -3.763932022

Simplifying
x = -3.763932022

Subproblem 2
x + 6 = -2.236067978

Simplifying
x + 6 = -2.236067978

Reorder the terms:
6 + x = -2.236067978

Solving
6 + x = -2.236067978

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -2.236067978 + -6

Combine like terms: 6 + -6 = 0
0 + x = -2.236067978 + -6
x = -2.236067978 + -6

Combine like terms: -2.236067978 + -6 = -8.236067978
x = -8.236067978

Simplifying
x = -8.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.763932022, -8.236067978}