=20x^2-20x+1

Solution for =20x^2-20x+1 equation:

Simplifying
0 = 20x2 + -20x + 1

Reorder the terms:
0 = 1 + -20x + 20x2

Solving
0 = 1 + -20x + 20x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 20x + -20x2 = 1 + -20x + 20x2 + -1 + 20x + -20x2

Reorder the terms:
-1 + 20x + -20x2 = 1 + -1 + -20x + 20x + 20x2 + -20x2

Combine like terms: 1 + -1 = 0
-1 + 20x + -20x2 = 0 + -20x + 20x + 20x2 + -20x2
-1 + 20x + -20x2 = -20x + 20x + 20x2 + -20x2

Combine like terms: -20x + 20x = 0
-1 + 20x + -20x2 = 0 + 20x2 + -20x2
-1 + 20x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-1 + 20x + -20x2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
0.05 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.05' to each side of the equation.
0.05 + -1x + -0.05 + x2 = 0 + -0.05

Reorder the terms:
0.05 + -0.05 + -1x + x2 = 0 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + -1x + x2 = 0 + -0.05
-1x + x2 = 0 + -0.05

Combine like terms: 0 + -0.05 = -0.05
-1x + x2 = -0.05

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 = -0.05 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.05 + 0.25

Combine like terms: -0.05 + 0.25 = 0.2
0.25 + -1x + x2 = 0.2

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.2

Calculate the square root of the right side: 0.447213596

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.447213596 and -0.447213596.

Subproblem 1
x + -0.5 = 0.447213596

Simplifying
x + -0.5 = 0.447213596

Reorder the terms:
-0.5 + x = 0.447213596

Solving
-0.5 + x = 0.447213596

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 = 0.447213596 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.447213596 + 0.5
x = 0.447213596 + 0.5

Combine like terms: 0.447213596 + 0.5 = 0.947213596
x = 0.947213596

Simplifying
x = 0.947213596

Subproblem 2
x + -0.5 = -0.447213596

Simplifying
x + -0.5 = -0.447213596

Reorder the terms:
-0.5 + x = -0.447213596

Solving
-0.5 + x = -0.447213596

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 = -0.447213596 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.447213596 + 0.5
x = -0.447213596 + 0.5

Combine like terms: -0.447213596 + 0.5 = 0.052786404
x = 0.052786404

Simplifying
x = 0.052786404

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.947213596, 0.052786404}