3*X^2+38*X+8=0

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Solution for 3*X^2+38*X+8=0 equation: 


Simplifying
3X2 + 38X + 8 = 0

Reorder the terms:
8 + 38X + 3X2 = 0

Solving
8 + 38X + 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'.
2.666666667 + 12.66666667X + X2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 12.66666667X + -2.666666667 + X2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 12.66666667X + X2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 12.66666667X + X2 = 0 + -2.666666667
12.66666667X + X2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
12.66666667X + X2 = -2.666666667

The X term is 12.66666667X.  Take half its coefficient (6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
12.66666667X + 40.11111113 + X2 = -2.666666667 + 40.11111113

Reorder the terms:
40.11111113 + 12.66666667X + X2 = -2.666666667 + 40.11111113

Combine like terms: -2.666666667 + 40.11111113 = 37.444444463
40.11111113 + 12.66666667X + X2 = 37.444444463

Factor a perfect square on the left side:
(X + 6.333333335)(X + 6.333333335) = 37.444444463

Calculate the square root of the right side: 6.119186585

Break this problem into two subproblems by setting 
(X + 6.333333335) equal to 6.119186585 and -6.119186585.


Subproblem 1
X + 6.333333335 = 6.119186585

Simplifying
X + 6.333333335 = 6.119186585

Reorder the terms:
6.333333335 + X = 6.119186585

Solving
6.333333335 + X = 6.119186585

Solving for variable 'X'.

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

Add '-6.333333335' to each side of the equation.
6.333333335 + -6.333333335 + X = 6.119186585 + -6.333333335

Combine like terms: 6.333333335 + -6.333333335 = 0.000000000
0.000000000 + X = 6.119186585 + -6.333333335
X = 6.119186585 + -6.333333335

Combine like terms: 6.119186585 + -6.333333335 = -0.21414675
X = -0.21414675

Simplifying
X = -0.21414675


Subproblem 2
X + 6.333333335 = -6.119186585

Simplifying
X + 6.333333335 = -6.119186585

Reorder the terms:
6.333333335 + X = -6.119186585

Solving
6.333333335 + X = -6.119186585

Solving for variable 'X'.

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

Add '-6.333333335' to each side of the equation.
6.333333335 + -6.333333335 + X = -6.119186585 + -6.333333335

Combine like terms: 6.333333335 + -6.333333335 = 0.000000000
0.000000000 + X = -6.119186585 + -6.333333335
X = -6.119186585 + -6.333333335

Combine like terms: -6.119186585 + -6.333333335 = -12.45251992
X = -12.45251992

Simplifying
X = -12.45251992


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.21414675, -12.45251992}

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