9x^2-12x-36=0

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Solution for 9x^2-12x-36=0 equation: 


Simplifying
9x2 + -12x + -36 = 0

Reorder the terms:
-36 + -12x + 9x2 = 0

Solving
-36 + -12x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -4x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-12 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-12 + -4x + 3x2 = 0

Solving
-12 + -4x + 3x2 = 0

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

Divide each side by '3'.
-4 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1.333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -1.333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1.333333333x + x2 = 0 + 4
-1.333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1.333333333x + x2 = 4

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 4 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 4 + 0.4444444442

Combine like terms: 4 + 0.4444444442 = 4.4444444442
0.4444444442 + -1.333333333x + x2 = 4.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 4.4444444442

Calculate the square root of the right side: 2.108185107

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 2.108185107 and -2.108185107.


Subproblem 1
x + -0.6666666665 = 2.108185107

Simplifying
x + -0.6666666665 = 2.108185107

Reorder the terms:
-0.6666666665 + x = 2.108185107

Solving
-0.6666666665 + x = 2.108185107

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 2.108185107 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 2.108185107 + 0.6666666665
x = 2.108185107 + 0.6666666665

Combine like terms: 2.108185107 + 0.6666666665 = 2.7748517735
x = 2.7748517735

Simplifying
x = 2.7748517735


Subproblem 2
x + -0.6666666665 = -2.108185107

Simplifying
x + -0.6666666665 = -2.108185107

Reorder the terms:
-0.6666666665 + x = -2.108185107

Solving
-0.6666666665 + x = -2.108185107

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -2.108185107 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -2.108185107 + 0.6666666665
x = -2.108185107 + 0.6666666665

Combine like terms: -2.108185107 + 0.6666666665 = -1.4415184405
x = -1.4415184405

Simplifying
x = -1.4415184405


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.7748517735, -1.4415184405}
Solution
x = {2.7748517735, -1.4415184405}

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