1x(2+2x)-(1+1x)=4

Solution for 1x(2+2x)-(1+1x)=4 equation:

Simplifying
1x(2 + 2x) + -1(1 + 1x) = 4
(2 * 1x + 2x * 1x) + -1(1 + 1x) = 4
(2x + 2x2) + -1(1 + 1x) = 4
2x + 2x2 + (1 * -1 + 1x * -1) = 4
2x + 2x2 + (-1 + -1x) = 4

Reorder the terms:
-1 + 2x + -1x + 2x2 = 4

Combine like terms: 2x + -1x = 1x
-1 + 1x + 2x2 = 4

Solving
-1 + 1x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
-1 + -4 + 1x + 2x2 = 4 + -4

Combine like terms: -1 + -4 = -5
-5 + 1x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-5 + 1x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.5x + x2 = 0 + 2.5
0.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.5x + x2 = 2.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 2.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + 0.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
x + 0.25 = 1.600781059

Simplifying
x + 0.25 = 1.600781059

Reorder the terms:
0.25 + x = 1.600781059

Solving
0.25 + x = 1.600781059

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.600781059 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.600781059 + -0.25
x = 1.600781059 + -0.25

Combine like terms: 1.600781059 + -0.25 = 1.350781059
x = 1.350781059

Simplifying
x = 1.350781059

Subproblem 2
x + 0.25 = -1.600781059

Simplifying
x + 0.25 = -1.600781059

Reorder the terms:
0.25 + x = -1.600781059

Solving
0.25 + x = -1.600781059

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.600781059 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.600781059 + -0.25
x = -1.600781059 + -0.25

Combine like terms: -1.600781059 + -0.25 = -1.850781059
x = -1.850781059

Simplifying
x = -1.850781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.350781059, -1.850781059}