-3x^2-22x-12=0

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Solution for -3x^2-22x-12=0 equation: 


Simplifying
-3x2 + -22x + -12 = 0

Reorder the terms:
-12 + -22x + -3x2 = 0

Solving
-12 + -22x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 22x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(12 + 22x + 3x2)' equal to zero and attempt to solve:

Simplifying
12 + 22x + 3x2 = 0

Solving
12 + 22x + 3x2 = 0

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

Divide each side by '3'.
4 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 7.333333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 7.333333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7.333333333x + x2 = 0 + -4
7.333333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
7.333333333x + x2 = -4

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = -4 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = -4 + 13.44444445

Combine like terms: -4 + 13.44444445 = 9.44444445
13.44444445 + 7.333333333x + x2 = 9.44444445

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 9.44444445

Calculate the square root of the right side: 3.073181487

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 3.073181487 and -3.073181487.


Subproblem 1
x + 3.666666667 = 3.073181487

Simplifying
x + 3.666666667 = 3.073181487

Reorder the terms:
3.666666667 + x = 3.073181487

Solving
3.666666667 + x = 3.073181487

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 3.073181487 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 3.073181487 + -3.666666667
x = 3.073181487 + -3.666666667

Combine like terms: 3.073181487 + -3.666666667 = -0.59348518
x = -0.59348518

Simplifying
x = -0.59348518


Subproblem 2
x + 3.666666667 = -3.073181487

Simplifying
x + 3.666666667 = -3.073181487

Reorder the terms:
3.666666667 + x = -3.073181487

Solving
3.666666667 + x = -3.073181487

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -3.073181487 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -3.073181487 + -3.666666667
x = -3.073181487 + -3.666666667

Combine like terms: -3.073181487 + -3.666666667 = -6.739848154
x = -6.739848154

Simplifying
x = -6.739848154


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.59348518, -6.739848154}
Solution
x = {-0.59348518, -6.739848154}

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