3x^2+52x+12=0

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Solution for 3x^2+52x+12=0 equation: 


Simplifying
3x2 + 52x + 12 = 0

Reorder the terms:
12 + 52x + 3x2 = 0

Solving
12 + 52x + 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 + 17.33333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 17.33333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 17.33333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 17.33333333x + x2 = 0 + -4
17.33333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
17.33333333x + x2 = -4

The x term is 17.33333333x.  Take half its coefficient (8.666666665).
Square it (75.11111108) and add it to both sides.

Add '75.11111108' to each side of the equation.
17.33333333x + 75.11111108 + x2 = -4 + 75.11111108

Reorder the terms:
75.11111108 + 17.33333333x + x2 = -4 + 75.11111108

Combine like terms: -4 + 75.11111108 = 71.11111108
75.11111108 + 17.33333333x + x2 = 71.11111108

Factor a perfect square on the left side:
(x + 8.666666665)(x + 8.666666665) = 71.11111108

Calculate the square root of the right side: 8.432740425

Break this problem into two subproblems by setting 
(x + 8.666666665) equal to 8.432740425 and -8.432740425.


Subproblem 1
x + 8.666666665 = 8.432740425

Simplifying
x + 8.666666665 = 8.432740425

Reorder the terms:
8.666666665 + x = 8.432740425

Solving
8.666666665 + x = 8.432740425

Solving for variable 'x'.

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

Add '-8.666666665' to each side of the equation.
8.666666665 + -8.666666665 + x = 8.432740425 + -8.666666665

Combine like terms: 8.666666665 + -8.666666665 = 0.000000000
0.000000000 + x = 8.432740425 + -8.666666665
x = 8.432740425 + -8.666666665

Combine like terms: 8.432740425 + -8.666666665 = -0.23392624
x = -0.23392624

Simplifying
x = -0.23392624


Subproblem 2
x + 8.666666665 = -8.432740425

Simplifying
x + 8.666666665 = -8.432740425

Reorder the terms:
8.666666665 + x = -8.432740425

Solving
8.666666665 + x = -8.432740425

Solving for variable 'x'.

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

Add '-8.666666665' to each side of the equation.
8.666666665 + -8.666666665 + x = -8.432740425 + -8.666666665

Combine like terms: 8.666666665 + -8.666666665 = 0.000000000
0.000000000 + x = -8.432740425 + -8.666666665
x = -8.432740425 + -8.666666665

Combine like terms: -8.432740425 + -8.666666665 = -17.09940709
x = -17.09940709

Simplifying
x = -17.09940709


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.23392624, -17.09940709}

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