2x^2-2x+1=0.55

Solution for 2x^2-2x+1=0.55 equation:

Simplifying
2x2 + -2x + 1 = 0.55

Reorder the terms:
1 + -2x + 2x2 = 0.55

Solving
1 + -2x + 2x2 = 0.55

Solving for variable 'x'.

Reorder the terms:
1 + -0.55 + -2x + 2x2 = 0.55 + -0.55

Combine like terms: 1 + -0.55 = 0.45
0.45 + -2x + 2x2 = 0.55 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.45 + -2x + 2x2 = 0.00

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

Divide each side by '2'.
0.225 + -1x + x2 = 0.00

Move the constant term to the right:

Add '-0.225' to each side of the equation.
0.225 + -1x + -0.225 + x2 = 0.00 + -0.225

Reorder the terms:
0.225 + -0.225 + -1x + x2 = 0.00 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + -1x + x2 = 0.00 + -0.225
-1x + x2 = 0.00 + -0.225

Combine like terms: 0.00 + -0.225 = -0.225
-1x + x2 = -0.225

The x term is -1x.  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 = -0.225 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.225 + 0.25

Combine like terms: -0.225 + 0.25 = 0.025
0.25 + -1x + x2 = 0.025

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.025

Calculate the square root of the right side: 0.158113883

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.158113883 and -0.158113883.

Subproblem 1
x + -0.5 = 0.158113883

Simplifying
x + -0.5 = 0.158113883

Reorder the terms:
-0.5 + x = 0.158113883

Solving
-0.5 + x = 0.158113883

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.158113883 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.158113883 + 0.5
x = 0.158113883 + 0.5

Combine like terms: 0.158113883 + 0.5 = 0.658113883
x = 0.658113883

Simplifying
x = 0.658113883

Subproblem 2
x + -0.5 = -0.158113883

Simplifying
x + -0.5 = -0.158113883

Reorder the terms:
-0.5 + x = -0.158113883

Solving
-0.5 + x = -0.158113883

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.158113883 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.158113883 + 0.5
x = -0.158113883 + 0.5

Combine like terms: -0.158113883 + 0.5 = 0.341886117
x = 0.341886117

Simplifying
x = 0.341886117

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.658113883, 0.341886117}