(36x^2)-12x-1=0

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Solution for (36x^2)-12x-1=0 equation: 


Simplifying
(36x2) + -12x + -1 = 0

Reorder the terms:
-1 + -12x + (36x2) = 0

Solving
-1 + -12x + (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 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.02777777778' to each side of the equation.
-0.02777777778 + -0.3333333333x + 0.02777777778 + x2 = 0 + 0.02777777778

Reorder the terms:
-0.02777777778 + 0.02777777778 + -0.3333333333x + x2 = 0 + 0.02777777778

Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000
0.00000000000 + -0.3333333333x + x2 = 0 + 0.02777777778
-0.3333333333x + x2 = 0 + 0.02777777778

Combine like terms: 0 + 0.02777777778 = 0.02777777778
-0.3333333333x + x2 = 0.02777777778

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 0.02777777778 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 0.02777777778 + 0.02777777779

Combine like terms: 0.02777777778 + 0.02777777779 = 0.05555555557
0.02777777779 + -0.3333333333x + x2 = 0.05555555557

Factor a perfect square on the left side:
((x) + -0.1666666667)((x) + -0.1666666667) = 0.05555555557

Calculate the square root of the right side: 0.23570226

Break this problem into two subproblems by setting 
((x) + -0.1666666667) equal to 0.23570226 and -0.23570226.


Subproblem 1
(x) + -0.1666666667 = 0.23570226

Simplifying
(x) + -0.1666666667 = 0.23570226
x + -0.1666666667 = 0.23570226

Reorder the terms:
-0.1666666667 + x = 0.23570226

Solving
-0.1666666667 + x = 0.23570226

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 0.23570226 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 0.23570226 + 0.1666666667
x = 0.23570226 + 0.1666666667

Combine like terms: 0.23570226 + 0.1666666667 = 0.4023689267
x = 0.4023689267

Simplifying
x = 0.4023689267


Subproblem 2
(x) + -0.1666666667 = -0.23570226

Simplifying
(x) + -0.1666666667 = -0.23570226
x + -0.1666666667 = -0.23570226

Reorder the terms:
-0.1666666667 + x = -0.23570226

Solving
-0.1666666667 + x = -0.23570226

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -0.23570226 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -0.23570226 + 0.1666666667
x = -0.23570226 + 0.1666666667

Combine like terms: -0.23570226 + 0.1666666667 = -0.0690355933
x = -0.0690355933

Simplifying
x = -0.0690355933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4023689267, -0.0690355933}

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