0.9x^2-1.9x+1=0

Solution for 0.9x^2-1.9x+1=0 equation:

Simplifying
0.9x2 + -1.9x + 1 = 0

Reorder the terms:
1 + -1.9x + 0.9x2 = 0

Solving
1 + -1.9x + 0.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.9'.
1.111111111 + -2.111111111x + x2 = 0

Move the constant term to the right:

Add '-1.111111111' to each side of the equation.
1.111111111 + -2.111111111x + -1.111111111 + x2 = 0 + -1.111111111

Reorder the terms:
1.111111111 + -1.111111111 + -2.111111111x + x2 = 0 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + -2.111111111x + x2 = 0 + -1.111111111
-2.111111111x + x2 = 0 + -1.111111111

Combine like terms: 0 + -1.111111111 = -1.111111111
-2.111111111x + x2 = -1.111111111

The x term is -2.111111111x.  Take half its coefficient (-1.055555556).
Square it (1.114197532) and add it to both sides.

Add '1.114197532' to each side of the equation.
-2.111111111x + 1.114197532 + x2 = -1.111111111 + 1.114197532

Reorder the terms:
1.114197532 + -2.111111111x + x2 = -1.111111111 + 1.114197532

Combine like terms: -1.111111111 + 1.114197532 = 0.003086421
1.114197532 + -2.111111111x + x2 = 0.003086421

Factor a perfect square on the left side:
(x + -1.055555556)(x + -1.055555556) = 0.003086421

Calculate the square root of the right side: 0.055555567

Break this problem into two subproblems by setting 
(x + -1.055555556) equal to 0.055555567 and -0.055555567.

Subproblem 1
x + -1.055555556 = 0.055555567

Simplifying
x + -1.055555556 = 0.055555567

Reorder the terms:
-1.055555556 + x = 0.055555567

Solving
-1.055555556 + x = 0.055555567

Solving for variable 'x'.

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

Add '1.055555556' to each side of the equation.
-1.055555556 + 1.055555556 + x = 0.055555567 + 1.055555556

Combine like terms: -1.055555556 + 1.055555556 = 0.000000000
0.000000000 + x = 0.055555567 + 1.055555556
x = 0.055555567 + 1.055555556

Combine like terms: 0.055555567 + 1.055555556 = 1.111111123
x = 1.111111123

Simplifying
x = 1.111111123

Subproblem 2
x + -1.055555556 = -0.055555567

Simplifying
x + -1.055555556 = -0.055555567

Reorder the terms:
-1.055555556 + x = -0.055555567

Solving
-1.055555556 + x = -0.055555567

Solving for variable 'x'.

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

Add '1.055555556' to each side of the equation.
-1.055555556 + 1.055555556 + x = -0.055555567 + 1.055555556

Combine like terms: -1.055555556 + 1.055555556 = 0.000000000
0.000000000 + x = -0.055555567 + 1.055555556
x = -0.055555567 + 1.055555556

Combine like terms: -0.055555567 + 1.055555556 = 0.999999989
x = 0.999999989

Simplifying
x = 0.999999989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.111111123, 0.999999989}