2y^2+11y+11=0

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Solution for 2y^2+11y+11=0 equation:


Simplifying
2y2 + 11y + 11 = 0

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

Solving
11 + 11y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
5.5 + 5.5y + y2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + 5.5y + -5.5 + y2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + 5.5y + y2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + 5.5y + y2 = 0 + -5.5
5.5y + y2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
5.5y + y2 = -5.5

The y term is 5.5y.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5y + 7.5625 + y2 = -5.5 + 7.5625

Reorder the terms:
7.5625 + 5.5y + y2 = -5.5 + 7.5625

Combine like terms: -5.5 + 7.5625 = 2.0625
7.5625 + 5.5y + y2 = 2.0625

Factor a perfect square on the left side:
(y + 2.75)(y + 2.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(y + 2.75) equal to 1.436140662 and -1.436140662.

Subproblem 1

y + 2.75 = 1.436140662 Simplifying y + 2.75 = 1.436140662 Reorder the terms: 2.75 + y = 1.436140662 Solving 2.75 + y = 1.436140662 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = 1.436140662 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = 1.436140662 + -2.75 y = 1.436140662 + -2.75 Combine like terms: 1.436140662 + -2.75 = -1.313859338 y = -1.313859338 Simplifying y = -1.313859338

Subproblem 2

y + 2.75 = -1.436140662 Simplifying y + 2.75 = -1.436140662 Reorder the terms: 2.75 + y = -1.436140662 Solving 2.75 + y = -1.436140662 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = -1.436140662 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = -1.436140662 + -2.75 y = -1.436140662 + -2.75 Combine like terms: -1.436140662 + -2.75 = -4.186140662 y = -4.186140662 Simplifying y = -4.186140662

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-1.313859338, -4.186140662}

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