36x^2-72x+1=0

Solution for 36x^2-72x+1=0 equation:

Simplifying
36x2 + -72x + 1 = 0

Reorder the terms:
1 + -72x + 36x2 = 0

Solving
1 + -72x + 36x2 = 0

Solving for variable 'x'.

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

Divide each side by '36'.
0.02777777778 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.02777777778' to each side of the equation.
0.02777777778 + -2x + -0.02777777778 + x2 = 0 + -0.02777777778

Reorder the terms:
0.02777777778 + -0.02777777778 + -2x + x2 = 0 + -0.02777777778

Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000
0.00000000000 + -2x + x2 = 0 + -0.02777777778
-2x + x2 = 0 + -0.02777777778

Combine like terms: 0 + -0.02777777778 = -0.02777777778
-2x + x2 = -0.02777777778

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 = -0.02777777778 + 1

Reorder the terms:
1 + -2x + x2 = -0.02777777778 + 1

Combine like terms: -0.02777777778 + 1 = 0.97222222222
1 + -2x + x2 = 0.97222222222

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.97222222222

Calculate the square root of the right side: 0.986013297

Break this problem into two subproblems by setting 
(x + -1) equal to 0.986013297 and -0.986013297.

Subproblem 1
x + -1 = 0.986013297

Simplifying
x + -1 = 0.986013297

Reorder the terms:
-1 + x = 0.986013297

Solving
-1 + x = 0.986013297

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 = 0.986013297 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.986013297 + 1
x = 0.986013297 + 1

Combine like terms: 0.986013297 + 1 = 1.986013297
x = 1.986013297

Simplifying
x = 1.986013297

Subproblem 2
x + -1 = -0.986013297

Simplifying
x + -1 = -0.986013297

Reorder the terms:
-1 + x = -0.986013297

Solving
-1 + x = -0.986013297

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 = -0.986013297 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.986013297 + 1
x = -0.986013297 + 1

Combine like terms: -0.986013297 + 1 = 0.013986703
x = 0.013986703

Simplifying
x = 0.013986703

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.986013297, 0.013986703}