36x^2-86x+36=0

Solution for 36x^2-86x+36=0 equation:

Simplifying
36x2 + -86x + 36 = 0

Reorder the terms:
36 + -86x + 36x2 = 0

Solving
36 + -86x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -43x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(18 + -43x + 18x2)' equal to zero and attempt to solve:

Simplifying
18 + -43x + 18x2 = 0

Solving
18 + -43x + 18x2 = 0

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

Divide each side by '18'.
1 + -2.388888889x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.388888889x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.388888889x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.388888889x + x2 = 0 + -1
-2.388888889x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.388888889x + x2 = -1

The x term is -2.388888889x.  Take half its coefficient (-1.194444445).
Square it (1.426697532) and add it to both sides.

Add '1.426697532' to each side of the equation.
-2.388888889x + 1.426697532 + x2 = -1 + 1.426697532

Reorder the terms:
1.426697532 + -2.388888889x + x2 = -1 + 1.426697532

Combine like terms: -1 + 1.426697532 = 0.426697532
1.426697532 + -2.388888889x + x2 = 0.426697532

Factor a perfect square on the left side:
(x + -1.194444445)(x + -1.194444445) = 0.426697532

Calculate the square root of the right side: 0.653220891

Break this problem into two subproblems by setting 
(x + -1.194444445) equal to 0.653220891 and -0.653220891.

Subproblem 1
x + -1.194444445 = 0.653220891

Simplifying
x + -1.194444445 = 0.653220891

Reorder the terms:
-1.194444445 + x = 0.653220891

Solving
-1.194444445 + x = 0.653220891

Solving for variable 'x'.

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

Add '1.194444445' to each side of the equation.
-1.194444445 + 1.194444445 + x = 0.653220891 + 1.194444445

Combine like terms: -1.194444445 + 1.194444445 = 0.000000000
0.000000000 + x = 0.653220891 + 1.194444445
x = 0.653220891 + 1.194444445

Combine like terms: 0.653220891 + 1.194444445 = 1.847665336
x = 1.847665336

Simplifying
x = 1.847665336

Subproblem 2
x + -1.194444445 = -0.653220891

Simplifying
x + -1.194444445 = -0.653220891

Reorder the terms:
-1.194444445 + x = -0.653220891

Solving
-1.194444445 + x = -0.653220891

Solving for variable 'x'.

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

Add '1.194444445' to each side of the equation.
-1.194444445 + 1.194444445 + x = -0.653220891 + 1.194444445

Combine like terms: -1.194444445 + 1.194444445 = 0.000000000
0.000000000 + x = -0.653220891 + 1.194444445
x = -0.653220891 + 1.194444445

Combine like terms: -0.653220891 + 1.194444445 = 0.541223554
x = 0.541223554

Simplifying
x = 0.541223554

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.847665336, 0.541223554}
Solution
x = {1.847665336, 0.541223554}