x(1-x)=0.2097

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Solution for x(1-x)=0.2097 equation: 


Simplifying
x(1 + -1x) = 0.2097
(1 * x + -1x * x) = 0.2097
(1x + -1x2) = 0.2097

Solving
1x + -1x2 = 0.2097

Solving for variable 'x'.

Reorder the terms:
-0.2097 + 1x + -1x2 = 0.2097 + -0.2097

Combine like terms: 0.2097 + -0.2097 = 0.0000
-0.2097 + 1x + -1x2 = 0.0000

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

Divide each side by '-1'.
0.2097 + -1x + x2 = 0.0000

Move the constant term to the right:

Add '-0.2097' to each side of the equation.
0.2097 + -1x + -0.2097 + x2 = 0.0000 + -0.2097

Reorder the terms:
0.2097 + -0.2097 + -1x + x2 = 0.0000 + -0.2097

Combine like terms: 0.2097 + -0.2097 = 0.0000
0.0000 + -1x + x2 = 0.0000 + -0.2097
-1x + x2 = 0.0000 + -0.2097

Combine like terms: 0.0000 + -0.2097 = -0.2097
-1x + x2 = -0.2097

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 = -0.2097 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.2097 + 0.25

Combine like terms: -0.2097 + 0.25 = 0.0403
0.25 + -1x + x2 = 0.0403

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.0403

Calculate the square root of the right side: 0.200748599

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.200748599 and -0.200748599.


Subproblem 1
x + -0.5 = 0.200748599

Simplifying
x + -0.5 = 0.200748599

Reorder the terms:
-0.5 + x = 0.200748599

Solving
-0.5 + x = 0.200748599

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 = 0.200748599 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.200748599 + 0.5
x = 0.200748599 + 0.5

Combine like terms: 0.200748599 + 0.5 = 0.700748599
x = 0.700748599

Simplifying
x = 0.700748599


Subproblem 2
x + -0.5 = -0.200748599

Simplifying
x + -0.5 = -0.200748599

Reorder the terms:
-0.5 + x = -0.200748599

Solving
-0.5 + x = -0.200748599

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 = -0.200748599 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.200748599 + 0.5
x = -0.200748599 + 0.5

Combine like terms: -0.200748599 + 0.5 = 0.299251401
x = 0.299251401

Simplifying
x = 0.299251401


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.700748599, 0.299251401}

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