36x^2-111x+16=0

Solution for 36x^2-111x+16=0 equation:

Simplifying
36x2 + -111x + 16 = 0

Reorder the terms:
16 + -111x + 36x2 = 0

Solving
16 + -111x + 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'.
0.4444444444 + -3.083333333x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -3.083333333x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -3.083333333x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -3.083333333x + x2 = 0 + -0.4444444444
-3.083333333x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-3.083333333x + x2 = -0.4444444444

The x term is -3.083333333x.  Take half its coefficient (-1.541666667).
Square it (2.376736112) and add it to both sides.

Add '2.376736112' to each side of the equation.
-3.083333333x + 2.376736112 + x2 = -0.4444444444 + 2.376736112

Reorder the terms:
2.376736112 + -3.083333333x + x2 = -0.4444444444 + 2.376736112

Combine like terms: -0.4444444444 + 2.376736112 = 1.9322916676
2.376736112 + -3.083333333x + x2 = 1.9322916676

Factor a perfect square on the left side:
(x + -1.541666667)(x + -1.541666667) = 1.9322916676

Calculate the square root of the right side: 1.390068943

Break this problem into two subproblems by setting 
(x + -1.541666667) equal to 1.390068943 and -1.390068943.

Subproblem 1
x + -1.541666667 = 1.390068943

Simplifying
x + -1.541666667 = 1.390068943

Reorder the terms:
-1.541666667 + x = 1.390068943

Solving
-1.541666667 + x = 1.390068943

Solving for variable 'x'.

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

Add '1.541666667' to each side of the equation.
-1.541666667 + 1.541666667 + x = 1.390068943 + 1.541666667

Combine like terms: -1.541666667 + 1.541666667 = 0.000000000
0.000000000 + x = 1.390068943 + 1.541666667
x = 1.390068943 + 1.541666667

Combine like terms: 1.390068943 + 1.541666667 = 2.93173561
x = 2.93173561

Simplifying
x = 2.93173561

Subproblem 2
x + -1.541666667 = -1.390068943

Simplifying
x + -1.541666667 = -1.390068943

Reorder the terms:
-1.541666667 + x = -1.390068943

Solving
-1.541666667 + x = -1.390068943

Solving for variable 'x'.

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

Add '1.541666667' to each side of the equation.
-1.541666667 + 1.541666667 + x = -1.390068943 + 1.541666667

Combine like terms: -1.541666667 + 1.541666667 = 0.000000000
0.000000000 + x = -1.390068943 + 1.541666667
x = -1.390068943 + 1.541666667

Combine like terms: -1.390068943 + 1.541666667 = 0.151597724
x = 0.151597724

Simplifying
x = 0.151597724

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.93173561, 0.151597724}