c(2-c)=.9

Solution for c(2-c)=.9 equation:

Simplifying
c(2 + -1c) = 0.9
(2 * c + -1c * c) = 0.9
(2c + -1c2) = 0.9

Solving
2c + -1c2 = 0.9

Solving for variable 'c'.

Reorder the terms:
-0.9 + 2c + -1c2 = 0.9 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
-0.9 + 2c + -1c2 = 0.0

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

Divide each side by '-1'.
0.9 + -2c + c2 = 0.0

Move the constant term to the right:

Add '-0.9' to each side of the equation.
0.9 + -2c + -0.9 + c2 = 0.0 + -0.9

Reorder the terms:
0.9 + -0.9 + -2c + c2 = 0.0 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + -2c + c2 = 0.0 + -0.9
-2c + c2 = 0.0 + -0.9

Combine like terms: 0.0 + -0.9 = -0.9
-2c + c2 = -0.9

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

Add '1' to each side of the equation.
-2c + 1 + c2 = -0.9 + 1

Reorder the terms:
1 + -2c + c2 = -0.9 + 1

Combine like terms: -0.9 + 1 = 0.1
1 + -2c + c2 = 0.1

Factor a perfect square on the left side:
(c + -1)(c + -1) = 0.1

Calculate the square root of the right side: 0.316227766

Break this problem into two subproblems by setting 
(c + -1) equal to 0.316227766 and -0.316227766.

Subproblem 1
c + -1 = 0.316227766

Simplifying
c + -1 = 0.316227766

Reorder the terms:
-1 + c = 0.316227766

Solving
-1 + c = 0.316227766

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 1 + c = 0.316227766 + 1

Combine like terms: -1 + 1 = 0
0 + c = 0.316227766 + 1
c = 0.316227766 + 1

Combine like terms: 0.316227766 + 1 = 1.316227766
c = 1.316227766

Simplifying
c = 1.316227766

Subproblem 2
c + -1 = -0.316227766

Simplifying
c + -1 = -0.316227766

Reorder the terms:
-1 + c = -0.316227766

Solving
-1 + c = -0.316227766

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 1 + c = -0.316227766 + 1

Combine like terms: -1 + 1 = 0
0 + c = -0.316227766 + 1
c = -0.316227766 + 1

Combine like terms: -0.316227766 + 1 = 0.683772234
c = 0.683772234

Simplifying
c = 0.683772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.316227766, 0.683772234}