6x^2+11x+1=0

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Solution for 6x^2+11x+1=0 equation: 


Simplifying
6x2 + 11x + 1 = 0

Reorder the terms:
1 + 11x + 6x2 = 0

Solving
1 + 11x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
0.1666666667 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 1.833333333x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 1.833333333x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 1.833333333x + x2 = 0 + -0.1666666667
1.833333333x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
1.833333333x + x2 = -0.1666666667

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = -0.1666666667 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = -0.1666666667 + 0.8402777775

Combine like terms: -0.1666666667 + 0.8402777775 = 0.6736111108
0.8402777775 + 1.833333333x + x2 = 0.6736111108

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 0.6736111108

Calculate the square root of the right side: 0.82073815

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 0.82073815 and -0.82073815.


Subproblem 1
x + 0.9166666665 = 0.82073815

Simplifying
x + 0.9166666665 = 0.82073815

Reorder the terms:
0.9166666665 + x = 0.82073815

Solving
0.9166666665 + x = 0.82073815

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = 0.82073815 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = 0.82073815 + -0.9166666665
x = 0.82073815 + -0.9166666665

Combine like terms: 0.82073815 + -0.9166666665 = -0.0959285165
x = -0.0959285165

Simplifying
x = -0.0959285165


Subproblem 2
x + 0.9166666665 = -0.82073815

Simplifying
x + 0.9166666665 = -0.82073815

Reorder the terms:
0.9166666665 + x = -0.82073815

Solving
0.9166666665 + x = -0.82073815

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = -0.82073815 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = -0.82073815 + -0.9166666665
x = -0.82073815 + -0.9166666665

Combine like terms: -0.82073815 + -0.9166666665 = -1.7374048165
x = -1.7374048165

Simplifying
x = -1.7374048165


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0959285165, -1.7374048165}

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