3x^2-27x-12=0

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Solution for 3x^2-27x-12=0 equation: 


Simplifying
3x2 + -27x + -12 = 0

Reorder the terms:
-12 + -27x + 3x2 = 0

Solving
-12 + -27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -9x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + -9x + x2 = 0

Solving
-4 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -9x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -9x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9x + x2 = 0 + 4
-9x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-9x + x2 = 4

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 4 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 4 + 20.25

Combine like terms: 4 + 20.25 = 24.25
20.25 + -9x + x2 = 24.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
x + -4.5 = 4.924428901

Simplifying
x + -4.5 = 4.924428901

Reorder the terms:
-4.5 + x = 4.924428901

Solving
-4.5 + x = 4.924428901

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.924428901 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.924428901 + 4.5
x = 4.924428901 + 4.5

Combine like terms: 4.924428901 + 4.5 = 9.424428901
x = 9.424428901

Simplifying
x = 9.424428901


Subproblem 2
x + -4.5 = -4.924428901

Simplifying
x + -4.5 = -4.924428901

Reorder the terms:
-4.5 + x = -4.924428901

Solving
-4.5 + x = -4.924428901

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.924428901 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.924428901 + 4.5
x = -4.924428901 + 4.5

Combine like terms: -4.924428901 + 4.5 = -0.424428901
x = -0.424428901

Simplifying
x = -0.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.424428901, -0.424428901}
Solution
x = {9.424428901, -0.424428901}

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