x-x^2-90=0

Solution for x-x^2-90=0 equation:

Simplifying
x + -1x2 + -90 = 0

Reorder the terms:
-90 + x + -1x2 = 0

Solving
-90 + x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
90 + -1x + x2 = 0

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + -1x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + -1x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + -1x + x2 = 0 + -90
-1x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
-1x + x2 = -90

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 = -90 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -90 + 0.25

Combine like terms: -90 + 0.25 = -89.75
0.25 + -1x + x2 = -89.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -89.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.