3x^2-36x-5=0

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Solution for 3x^2-36x-5=0 equation: 


Simplifying
3x2 + -36x + -5 = 0

Reorder the terms:
-5 + -36x + 3x2 = 0

Solving
-5 + -36x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-1.666666667 + -12x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -12x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -12x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -12x + x2 = 0 + 1.666666667
-12x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-12x + x2 = 1.666666667

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 1.666666667 + 36

Reorder the terms:
36 + -12x + x2 = 1.666666667 + 36

Combine like terms: 1.666666667 + 36 = 37.666666667
36 + -12x + x2 = 37.666666667

Factor a perfect square on the left side:
(x + -6)(x + -6) = 37.666666667

Calculate the square root of the right side: 6.137317547

Break this problem into two subproblems by setting 
(x + -6) equal to 6.137317547 and -6.137317547.


Subproblem 1
x + -6 = 6.137317547

Simplifying
x + -6 = 6.137317547

Reorder the terms:
-6 + x = 6.137317547

Solving
-6 + x = 6.137317547

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 6.137317547 + 6

Combine like terms: -6 + 6 = 0
0 + x = 6.137317547 + 6
x = 6.137317547 + 6

Combine like terms: 6.137317547 + 6 = 12.137317547
x = 12.137317547

Simplifying
x = 12.137317547


Subproblem 2
x + -6 = -6.137317547

Simplifying
x + -6 = -6.137317547

Reorder the terms:
-6 + x = -6.137317547

Solving
-6 + x = -6.137317547

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -6.137317547 + 6

Combine like terms: -6 + 6 = 0
0 + x = -6.137317547 + 6
x = -6.137317547 + 6

Combine like terms: -6.137317547 + 6 = -0.137317547
x = -0.137317547

Simplifying
x = -0.137317547


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.137317547, -0.137317547}

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