0.24=x-x^2

Solution for 0.24=x-x^2 equation:

Simplifying
0.24 = x + -1x2

Solving
0.24 = x + -1x2

Solving for variable 'x'.

Reorder the terms:
0.24 + -1x + x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
0.24 + -1x + x2 = 0 + -1x2 + x2
0.24 + -1x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
0.24 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-0.24' to each side of the equation.
0.24 + -1x + -0.24 + x2 = 0 + -0.24

Reorder the terms:
0.24 + -0.24 + -1x + x2 = 0 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + -1x + x2 = 0 + -0.24
-1x + x2 = 0 + -0.24

Combine like terms: 0 + -0.24 = -0.24
-1x + x2 = -0.24

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 = -0.24 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.24 + 0.25

Combine like terms: -0.24 + 0.25 = 0.01
0.25 + -1x + x2 = 0.01

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.1 and -0.1.

Subproblem 1
x + -0.5 = 0.1

Simplifying
x + -0.5 = 0.1

Reorder the terms:
-0.5 + x = 0.1

Solving
-0.5 + x = 0.1

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 = 0.1 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.1 + 0.5
x = 0.1 + 0.5

Combine like terms: 0.1 + 0.5 = 0.6
x = 0.6

Simplifying
x = 0.6

Subproblem 2
x + -0.5 = -0.1

Simplifying
x + -0.5 = -0.1

Reorder the terms:
-0.5 + x = -0.1

Solving
-0.5 + x = -0.1

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 = -0.1 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.1 + 0.5
x = -0.1 + 0.5

Combine like terms: -0.1 + 0.5 = 0.4
x = 0.4

Simplifying
x = 0.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6, 0.4}