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

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

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

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

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

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

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

Solving
1 + 2x = 1x + 1x2

Solving for variable 'x'.

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

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

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -1x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = 1 + 0.25

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

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1x + x2 = 1.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + -0.5 = 1.118033989

Simplifying
x + -0.5 = 1.118033989

Reorder the terms:
-0.5 + x = 1.118033989

Solving
-0.5 + x = 1.118033989

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 = 1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.118033989 + 0.5
x = 1.118033989 + 0.5

Combine like terms: 1.118033989 + 0.5 = 1.618033989
x = 1.618033989

Simplifying
x = 1.618033989

Subproblem 2
x + -0.5 = -1.118033989

Simplifying
x + -0.5 = -1.118033989

Reorder the terms:
-0.5 + x = -1.118033989

Solving
-0.5 + x = -1.118033989

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 = -1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.118033989 + 0.5
x = -1.118033989 + 0.5

Combine like terms: -1.118033989 + 0.5 = -0.618033989
x = -0.618033989

Simplifying
x = -0.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.618033989, -0.618033989}