2x(1-x)+2=x-7(1-x)x

Solution for 2x(1-x)+2=x-7(1-x)x equation:

Simplifying
2x(1 + -1x) + 2 = x + -7(1 + -1x) * x
(1 * 2x + -1x * 2x) + 2 = x + -7(1 + -1x) * x
(2x + -2x2) + 2 = x + -7(1 + -1x) * x

Reorder the terms:
2 + 2x + -2x2 = x + -7(1 + -1x) * x

Reorder the terms for easier multiplication:
2 + 2x + -2x2 = x + -7x(1 + -1x)
2 + 2x + -2x2 = x + (1 * -7x + -1x * -7x)
2 + 2x + -2x2 = x + (-7x + 7x2)

Combine like terms: x + -7x = -6x
2 + 2x + -2x2 = -6x + 7x2

Solving
2 + 2x + -2x2 = -6x + 7x2

Solving for variable 'x'.

Reorder the terms:
2 + 2x + 6x + -2x2 + -7x2 = -6x + 7x2 + 6x + -7x2

Combine like terms: 2x + 6x = 8x
2 + 8x + -2x2 + -7x2 = -6x + 7x2 + 6x + -7x2

Combine like terms: -2x2 + -7x2 = -9x2
2 + 8x + -9x2 = -6x + 7x2 + 6x + -7x2

Reorder the terms:
2 + 8x + -9x2 = -6x + 6x + 7x2 + -7x2

Combine like terms: -6x + 6x = 0
2 + 8x + -9x2 = 0 + 7x2 + -7x2
2 + 8x + -9x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
2 + 8x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.2222222222 + -0.8888888889x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.8888888889x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.8888888889x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.8888888889x + x2 = 0 + 0.2222222222
-0.8888888889x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.8888888889x + x2 = 0.2222222222

The x term is -0.8888888889x.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889x + 0.1975308642 + x2 = 0.2222222222 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889x + x2 = 0.2222222222 + 0.1975308642

Combine like terms: 0.2222222222 + 0.1975308642 = 0.4197530864
0.1975308642 + -0.8888888889x + x2 = 0.4197530864

Factor a perfect square on the left side:
(x + -0.4444444445)(x + -0.4444444445) = 0.4197530864

Calculate the square root of the right side: 0.647883544

Break this problem into two subproblems by setting 
(x + -0.4444444445) equal to 0.647883544 and -0.647883544.

Subproblem 1
x + -0.4444444445 = 0.647883544

Simplifying
x + -0.4444444445 = 0.647883544

Reorder the terms:
-0.4444444445 + x = 0.647883544

Solving
-0.4444444445 + x = 0.647883544

Solving for variable 'x'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + x = 0.647883544 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = 0.647883544 + 0.4444444445
x = 0.647883544 + 0.4444444445

Combine like terms: 0.647883544 + 0.4444444445 = 1.0923279885
x = 1.0923279885

Simplifying
x = 1.0923279885

Subproblem 2
x + -0.4444444445 = -0.647883544

Simplifying
x + -0.4444444445 = -0.647883544

Reorder the terms:
-0.4444444445 + x = -0.647883544

Solving
-0.4444444445 + x = -0.647883544

Solving for variable 'x'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + x = -0.647883544 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = -0.647883544 + 0.4444444445
x = -0.647883544 + 0.4444444445

Combine like terms: -0.647883544 + 0.4444444445 = -0.2034390995
x = -0.2034390995

Simplifying
x = -0.2034390995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0923279885, -0.2034390995}