6a^2+11a+2=0

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Solution for 6a^2+11a+2=0 equation: 


Simplifying
6a2 + 11a + 2 = 0

Reorder the terms:
2 + 11a + 6a2 = 0

Solving
2 + 11a + 6a2 = 0

Solving for variable 'a'.

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

Divide each side by '6'.
0.3333333333 + 1.833333333a + a2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 1.833333333a + -0.3333333333 + a2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 1.833333333a + a2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 1.833333333a + a2 = 0 + -0.3333333333
1.833333333a + a2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
1.833333333a + a2 = -0.3333333333

The a term is 1.833333333a.  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.
1.833333333a + 0.8402777775 + a2 = -0.3333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333a + a2 = -0.3333333333 + 0.8402777775

Combine like terms: -0.3333333333 + 0.8402777775 = 0.5069444442
0.8402777775 + 1.833333333a + a2 = 0.5069444442

Factor a perfect square on the left side:
(a + 0.9166666665)(a + 0.9166666665) = 0.5069444442

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(a + 0.9166666665) equal to 0.712000312 and -0.712000312.


Subproblem 1
a + 0.9166666665 = 0.712000312

Simplifying
a + 0.9166666665 = 0.712000312

Reorder the terms:
0.9166666665 + a = 0.712000312

Solving
0.9166666665 + a = 0.712000312

Solving for variable 'a'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + a = 0.712000312 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + a = 0.712000312 + -0.9166666665
a = 0.712000312 + -0.9166666665

Combine like terms: 0.712000312 + -0.9166666665 = -0.2046663545
a = -0.2046663545

Simplifying
a = -0.2046663545


Subproblem 2
a + 0.9166666665 = -0.712000312

Simplifying
a + 0.9166666665 = -0.712000312

Reorder the terms:
0.9166666665 + a = -0.712000312

Solving
0.9166666665 + a = -0.712000312

Solving for variable 'a'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + a = -0.712000312 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + a = -0.712000312 + -0.9166666665
a = -0.712000312 + -0.9166666665

Combine like terms: -0.712000312 + -0.9166666665 = -1.6286669785
a = -1.6286669785

Simplifying
a = -1.6286669785


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.2046663545, -1.6286669785}

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