3x^2=-12x-2

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


Simplifying
3x2 = -12x + -2

Reorder the terms:
3x2 = -2 + -12x

Solving
3x2 = -2 + -12x

Solving for variable 'x'.

Reorder the terms:
2 + 12x + 3x2 = -2 + -12x + 2 + 12x

Reorder the terms:
2 + 12x + 3x2 = -2 + 2 + -12x + 12x

Combine like terms: -2 + 2 = 0
2 + 12x + 3x2 = 0 + -12x + 12x
2 + 12x + 3x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
2 + 12x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + 4x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 4x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 4x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 4x + x2 = 0 + -0.6666666667
4x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
4x + x2 = -0.6666666667

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -0.6666666667 + 4

Reorder the terms:
4 + 4x + x2 = -0.6666666667 + 4

Combine like terms: -0.6666666667 + 4 = 3.3333333333
4 + 4x + x2 = 3.3333333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 3.3333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(x + 2) equal to 1.825741858 and -1.825741858.


Subproblem 1
x + 2 = 1.825741858

Simplifying
x + 2 = 1.825741858

Reorder the terms:
2 + x = 1.825741858

Solving
2 + x = 1.825741858

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 1.825741858 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.825741858 + -2
x = 1.825741858 + -2

Combine like terms: 1.825741858 + -2 = -0.174258142
x = -0.174258142

Simplifying
x = -0.174258142


Subproblem 2
x + 2 = -1.825741858

Simplifying
x + 2 = -1.825741858

Reorder the terms:
2 + x = -1.825741858

Solving
2 + x = -1.825741858

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -1.825741858 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.825741858 + -2
x = -1.825741858 + -2

Combine like terms: -1.825741858 + -2 = -3.825741858
x = -3.825741858

Simplifying
x = -3.825741858


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.174258142, -3.825741858}

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