x-x^2=0.5

Solution for x-x^2=0.5 equation:

Simplifying
x + -1x2 = 0.5

Solving
x + -1x2 = 0.5

Solving for variable 'x'.

Reorder the terms:
-0.5 + x + -1x2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + x + -1x2 = 0.0

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

Divide each side by '-1'.
0.5 + -1x + x2 = 0.0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1x + -0.5 + x2 = 0.0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1x + x2 = 0.0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1x + x2 = 0.0 + -0.5
-1x + x2 = 0.0 + -0.5

Combine like terms: 0.0 + -0.5 = -0.5
-1x + x2 = -0.5

The x term is x.  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 = -0.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + -1x + x2 = -0.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.