3x^2+31x+8=0

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Solution for 3x^2+31x+8=0 equation: 


Simplifying
3x2 + 31x + 8 = 0

Reorder the terms:
8 + 31x + 3x2 = 0

Solving
8 + 31x + 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 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 10.33333333x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 10.33333333x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 10.33333333x + x2 = 0 + -2.666666667
10.33333333x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
10.33333333x + x2 = -2.666666667

The x term is 10.33333333x.  Take half its coefficient (5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
10.33333333x + 26.69444443 + x2 = -2.666666667 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = -2.666666667 + 26.69444443

Combine like terms: -2.666666667 + 26.69444443 = 24.027777763
26.69444443 + 10.33333333x + x2 = 24.027777763

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 24.027777763

Calculate the square root of the right side: 4.901813722

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 4.901813722 and -4.901813722.


Subproblem 1
x + 5.166666665 = 4.901813722

Simplifying
x + 5.166666665 = 4.901813722

Reorder the terms:
5.166666665 + x = 4.901813722

Solving
5.166666665 + x = 4.901813722

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = 4.901813722 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 4.901813722 + -5.166666665
x = 4.901813722 + -5.166666665

Combine like terms: 4.901813722 + -5.166666665 = -0.264852943
x = -0.264852943

Simplifying
x = -0.264852943


Subproblem 2
x + 5.166666665 = -4.901813722

Simplifying
x + 5.166666665 = -4.901813722

Reorder the terms:
5.166666665 + x = -4.901813722

Solving
5.166666665 + x = -4.901813722

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = -4.901813722 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -4.901813722 + -5.166666665
x = -4.901813722 + -5.166666665

Combine like terms: -4.901813722 + -5.166666665 = -10.068480387
x = -10.068480387

Simplifying
x = -10.068480387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.264852943, -10.068480387}

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