6x^2+24x+8=0

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Solution for 6x^2+24x+8=0 equation: 


Simplifying
6x2 + 24x + 8 = 0

Reorder the terms:
8 + 24x + 6x2 = 0

Solving
8 + 24x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 12x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 12x + 3x2 = 0

Solving
4 + 12x + 3x2 = 0

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}
Solution
x = {-0.367006838, -3.632993162}

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