3x^2+40x+12=0

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Solution for 3x^2+40x+12=0 equation: 


Simplifying
3x2 + 40x + 12 = 0

Reorder the terms:
12 + 40x + 3x2 = 0

Solving
12 + 40x + 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'.
4 + 13.33333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 13.33333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 13.33333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 13.33333333x + x2 = 0 + -4
13.33333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
13.33333333x + x2 = -4

The x term is 13.33333333x.  Take half its coefficient (6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
13.33333333x + 44.44444442 + x2 = -4 + 44.44444442

Reorder the terms:
44.44444442 + 13.33333333x + x2 = -4 + 44.44444442

Combine like terms: -4 + 44.44444442 = 40.44444442
44.44444442 + 13.33333333x + x2 = 40.44444442

Factor a perfect square on the left side:
(x + 6.666666665)(x + 6.666666665) = 40.44444442

Calculate the square root of the right side: 6.359594674

Break this problem into two subproblems by setting 
(x + 6.666666665) equal to 6.359594674 and -6.359594674.


Subproblem 1
x + 6.666666665 = 6.359594674

Simplifying
x + 6.666666665 = 6.359594674

Reorder the terms:
6.666666665 + x = 6.359594674

Solving
6.666666665 + x = 6.359594674

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = 6.359594674 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = 6.359594674 + -6.666666665
x = 6.359594674 + -6.666666665

Combine like terms: 6.359594674 + -6.666666665 = -0.307071991
x = -0.307071991

Simplifying
x = -0.307071991


Subproblem 2
x + 6.666666665 = -6.359594674

Simplifying
x + 6.666666665 = -6.359594674

Reorder the terms:
6.666666665 + x = -6.359594674

Solving
6.666666665 + x = -6.359594674

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = -6.359594674 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = -6.359594674 + -6.666666665
x = -6.359594674 + -6.666666665

Combine like terms: -6.359594674 + -6.666666665 = -13.026261339
x = -13.026261339

Simplifying
x = -13.026261339


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.307071991, -13.026261339}

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