6y^2+11y+2=

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Solution for 6y^2+11y+2= equation:


Simplifying
6y2 + 11y + 2 = 0

Reorder the terms:
2 + 11y + 6y2 = 0

Solving
2 + 11y + 6y2 = 0

Solving for variable 'y'.

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

Divide each side by '6'.
0.3333333333 + 1.833333333y + y2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 1.833333333y + -0.3333333333 + y2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 1.833333333y + y2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 1.833333333y + y2 = 0 + -0.3333333333
1.833333333y + y2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
1.833333333y + y2 = -0.3333333333

The y term is 1.833333333y.  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.
1.833333333y + 0.8402777775 + y2 = -0.3333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333y + y2 = -0.3333333333 + 0.8402777775

Combine like terms: -0.3333333333 + 0.8402777775 = 0.5069444442
0.8402777775 + 1.833333333y + y2 = 0.5069444442

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

Calculate the square root of the right side: 0.712000312

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

Subproblem 1

y + 0.9166666665 = 0.712000312 Simplifying y + 0.9166666665 = 0.712000312 Reorder the terms: 0.9166666665 + y = 0.712000312 Solving 0.9166666665 + y = 0.712000312 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + y = 0.712000312 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + y = 0.712000312 + -0.9166666665 y = 0.712000312 + -0.9166666665 Combine like terms: 0.712000312 + -0.9166666665 = -0.2046663545 y = -0.2046663545 Simplifying y = -0.2046663545

Subproblem 2

y + 0.9166666665 = -0.712000312 Simplifying y + 0.9166666665 = -0.712000312 Reorder the terms: 0.9166666665 + y = -0.712000312 Solving 0.9166666665 + y = -0.712000312 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + y = -0.712000312 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + y = -0.712000312 + -0.9166666665 y = -0.712000312 + -0.9166666665 Combine like terms: -0.712000312 + -0.9166666665 = -1.6286669785 y = -1.6286669785 Simplifying y = -1.6286669785

Solution

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

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