3x(x+4)+4=0

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Solution for 3x(x+4)+4=0 equation: 


Simplifying
3x(x + 4) + 4 = 0

Reorder the terms:
3x(4 + x) + 4 = 0
(4 * 3x + x * 3x) + 4 = 0
(12x + 3x2) + 4 = 0

Reorder the terms:
4 + 12x + 3x2 = 0

Solving
4 + 12x + 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'.
1.333333333 + 4x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 4x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 4x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 4x + x2 = 0 + -1.333333333
4x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
4x + x2 = -1.333333333

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 = -1.333333333 + 4

Reorder the terms:
4 + 4x + x2 = -1.333333333 + 4

Combine like terms: -1.333333333 + 4 = 2.666666667
4 + 4x + x2 = 2.666666667

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(x + 2) equal to 1.632993162 and -1.632993162.


Subproblem 1
x + 2 = 1.632993162

Simplifying
x + 2 = 1.632993162

Reorder the terms:
2 + x = 1.632993162

Solving
2 + x = 1.632993162

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 = 1.632993162 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.632993162 + -2
x = 1.632993162 + -2

Combine like terms: 1.632993162 + -2 = -0.367006838
x = -0.367006838

Simplifying
x = -0.367006838


Subproblem 2
x + 2 = -1.632993162

Simplifying
x + 2 = -1.632993162

Reorder the terms:
2 + x = -1.632993162

Solving
2 + x = -1.632993162

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 = -1.632993162 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.632993162 + -2
x = -1.632993162 + -2

Combine like terms: -1.632993162 + -2 = -3.632993162
x = -3.632993162

Simplifying
x = -3.632993162


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.367006838, -3.632993162}

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