3x^2-36x-12=0

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Solution for 3x^2-36x-12=0 equation: 


Simplifying
3x2 + -36x + -12 = 0

Reorder the terms:
-12 + -36x + 3x2 = 0

Solving
-12 + -36x + 3x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

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

Simplifying
-4 + -12x + x2 = 0

Solving
-4 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -12x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -12x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -12x + x2 = 0 + 4
-12x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-12x + x2 = 4

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 = 4 + 36

Reorder the terms:
36 + -12x + x2 = 4 + 36

Combine like terms: 4 + 36 = 40
36 + -12x + x2 = 40

Factor a perfect square on the left side:
(x + -6)(x + -6) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -6) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -6 = 6.32455532

Simplifying
x + -6 = 6.32455532

Reorder the terms:
-6 + x = 6.32455532

Solving
-6 + x = 6.32455532

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 = 6.32455532 + 6

Combine like terms: -6 + 6 = 0
0 + x = 6.32455532 + 6
x = 6.32455532 + 6

Combine like terms: 6.32455532 + 6 = 12.32455532
x = 12.32455532

Simplifying
x = 12.32455532


Subproblem 2
x + -6 = -6.32455532

Simplifying
x + -6 = -6.32455532

Reorder the terms:
-6 + x = -6.32455532

Solving
-6 + x = -6.32455532

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 = -6.32455532 + 6

Combine like terms: -6 + 6 = 0
0 + x = -6.32455532 + 6
x = -6.32455532 + 6

Combine like terms: -6.32455532 + 6 = -0.32455532
x = -0.32455532

Simplifying
x = -0.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.32455532, -0.32455532}
Solution
x = {12.32455532, -0.32455532}

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