x-x^2=1

Solution for x-x^2=1 equation:

Simplifying
x + -1x2 = 1

Solving
x + -1x2 = 1

Solving for variable 'x'.

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

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

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

Divide each side by '-1'.
1 + -1x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = -1 + 0.25

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

Combine like terms: -1 + 0.25 = -0.75
0.25 + -1x + x2 = -0.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.