0.1824=x-x^2

Solution for 0.1824=x-x^2 equation:

Simplifying
0.1824 = x + -1x2

Solving
0.1824 = x + -1x2

Solving for variable 'x'.

Reorder the terms:
0.1824 + -1x + x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
0.1824 + -1x + x2 = 0 + -1x2 + x2
0.1824 + -1x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
0.1824 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-0.1824' to each side of the equation.
0.1824 + -1x + -0.1824 + x2 = 0 + -0.1824

Reorder the terms:
0.1824 + -0.1824 + -1x + x2 = 0 + -0.1824

Combine like terms: 0.1824 + -0.1824 = 0.0000
0.0000 + -1x + x2 = 0 + -0.1824
-1x + x2 = 0 + -0.1824

Combine like terms: 0 + -0.1824 = -0.1824
-1x + x2 = -0.1824

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 = -0.1824 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.1824 + 0.25

Combine like terms: -0.1824 + 0.25 = 0.0676
0.25 + -1x + x2 = 0.0676

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.0676

Calculate the square root of the right side: 0.26

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.26 and -0.26.

Subproblem 1
x + -0.5 = 0.26

Simplifying
x + -0.5 = 0.26

Reorder the terms:
-0.5 + x = 0.26

Solving
-0.5 + x = 0.26

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 = 0.26 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.26 + 0.5
x = 0.26 + 0.5

Combine like terms: 0.26 + 0.5 = 0.76
x = 0.76

Simplifying
x = 0.76

Subproblem 2
x + -0.5 = -0.26

Simplifying
x + -0.5 = -0.26

Reorder the terms:
-0.5 + x = -0.26

Solving
-0.5 + x = -0.26

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 = -0.26 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.26 + 0.5
x = -0.26 + 0.5

Combine like terms: -0.26 + 0.5 = 0.24
x = 0.24

Simplifying
x = 0.24

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.76, 0.24}