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

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


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

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

Combine like terms: -2x + -2x = -4x
(2 + -4x + 2x2) = 4

Solving
2 + -4x + 2x2 = 4

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + -2x + x2 = 0

Solving
-1 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -2x + x2 = 0 + 1

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

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

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1 + 1

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

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

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -1) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + -1 = 1.414213562

Simplifying
x + -1 = 1.414213562

Reorder the terms:
-1 + x = 1.414213562

Solving
-1 + x = 1.414213562

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.414213562 + 1
x = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
x = 2.414213562

Simplifying
x = 2.414213562


Subproblem 2
x + -1 = -1.414213562

Simplifying
x + -1 = -1.414213562

Reorder the terms:
-1 + x = -1.414213562

Solving
-1 + x = -1.414213562

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.414213562 + 1
x = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
x = -0.414213562

Simplifying
x = -0.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.414213562, -0.414213562}
Solution
x = {2.414213562, -0.414213562}

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