0=-x^2+1.66x-.55

Solution for 0=-x^2+1.66x-.55 equation:

Simplifying
0 = -1x2 + 1.66x + -0.55

Reorder the terms:
0 = -0.55 + 1.66x + -1x2

Solving
0 = -0.55 + 1.66x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 0.55 = 0.55
0.55 + -1.66x + x2 = -0.55 + 1.66x + -1x2 + 0.55 + -1.66x + x2

Reorder the terms:
0.55 + -1.66x + x2 = -0.55 + 0.55 + 1.66x + -1.66x + -1x2 + x2

Combine like terms: -0.55 + 0.55 = 0.00
0.55 + -1.66x + x2 = 0.00 + 1.66x + -1.66x + -1x2 + x2
0.55 + -1.66x + x2 = 1.66x + -1.66x + -1x2 + x2

Combine like terms: 1.66x + -1.66x = 0.00
0.55 + -1.66x + x2 = 0.00 + -1x2 + x2
0.55 + -1.66x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
0.55 + -1.66x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-0.55' to each side of the equation.
0.55 + -1.66x + -0.55 + x2 = 0 + -0.55

Reorder the terms:
0.55 + -0.55 + -1.66x + x2 = 0 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + -1.66x + x2 = 0 + -0.55
-1.66x + x2 = 0 + -0.55

Combine like terms: 0 + -0.55 = -0.55
-1.66x + x2 = -0.55

The x term is -1.66x.  Take half its coefficient (-0.83).
Square it (0.6889) and add it to both sides.

Add '0.6889' to each side of the equation.
-1.66x + 0.6889 + x2 = -0.55 + 0.6889

Reorder the terms:
0.6889 + -1.66x + x2 = -0.55 + 0.6889

Combine like terms: -0.55 + 0.6889 = 0.1389
0.6889 + -1.66x + x2 = 0.1389

Factor a perfect square on the left side:
(x + -0.83)(x + -0.83) = 0.1389

Calculate the square root of the right side: 0.372692903

Break this problem into two subproblems by setting 
(x + -0.83) equal to 0.372692903 and -0.372692903.

Subproblem 1
x + -0.83 = 0.372692903

Simplifying
x + -0.83 = 0.372692903

Reorder the terms:
-0.83 + x = 0.372692903

Solving
-0.83 + x = 0.372692903

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.83' to each side of the equation.
-0.83 + 0.83 + x = 0.372692903 + 0.83

Combine like terms: -0.83 + 0.83 = 0.00
0.00 + x = 0.372692903 + 0.83
x = 0.372692903 + 0.83

Combine like terms: 0.372692903 + 0.83 = 1.202692903
x = 1.202692903

Simplifying
x = 1.202692903

Subproblem 2
x + -0.83 = -0.372692903

Simplifying
x + -0.83 = -0.372692903

Reorder the terms:
-0.83 + x = -0.372692903

Solving
-0.83 + x = -0.372692903

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.83' to each side of the equation.
-0.83 + 0.83 + x = -0.372692903 + 0.83

Combine like terms: -0.83 + 0.83 = 0.00
0.00 + x = -0.372692903 + 0.83
x = -0.372692903 + 0.83

Combine like terms: -0.372692903 + 0.83 = 0.457307097
x = 0.457307097

Simplifying
x = 0.457307097

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.202692903, 0.457307097}