10x^2-20x+1=0

Solution for 10x^2-20x+1=0 equation:

Simplifying
10x2 + -20x + 1 = 0

Reorder the terms:
1 + -20x + 10x2 = 0

Solving
1 + -20x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
0.1 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -2x + -0.1 + x2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + -2x + x2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -2x + x2 = 0 + -0.1
-2x + x2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
-2x + x2 = -0.1

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.1 + 1

Reorder the terms:
1 + -2x + x2 = -0.1 + 1

Combine like terms: -0.1 + 1 = 0.9
1 + -2x + x2 = 0.9

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.9

Calculate the square root of the right side: 0.948683298

Break this problem into two subproblems by setting 
(x + -1) equal to 0.948683298 and -0.948683298.

Subproblem 1
x + -1 = 0.948683298

Simplifying
x + -1 = 0.948683298

Reorder the terms:
-1 + x = 0.948683298

Solving
-1 + x = 0.948683298

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.948683298 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.948683298 + 1
x = 0.948683298 + 1

Combine like terms: 0.948683298 + 1 = 1.948683298
x = 1.948683298

Simplifying
x = 1.948683298

Subproblem 2
x + -1 = -0.948683298

Simplifying
x + -1 = -0.948683298

Reorder the terms:
-1 + x = -0.948683298

Solving
-1 + x = -0.948683298

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.948683298 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.948683298 + 1
x = -0.948683298 + 1

Combine like terms: -0.948683298 + 1 = 0.051316702
x = 0.051316702

Simplifying
x = 0.051316702

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.948683298, 0.051316702}