2y^2+10y=-11

Solution for 2y^2+10y=-11 equation:

Simplifying
2y2 + 10y = -11

Reorder the terms:
10y + 2y2 = -11

Solving
10y + 2y2 = -11

Solving for variable 'y'.

Reorder the terms:
11 + 10y + 2y2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + 10y + 2y2 = 0

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

Divide each side by '2'.
5.5 + 5y + y2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + 5y + -5.5 + y2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + 5y + y2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + 5y + y2 = 0 + -5.5
5y + y2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
5y + y2 = -5.5

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = -5.5 + 6.25

Reorder the terms:
6.25 + 5y + y2 = -5.5 + 6.25

Combine like terms: -5.5 + 6.25 = 0.75
6.25 + 5y + y2 = 0.75

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(y + 2.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
y + 2.5 = 0.866025404

Simplifying
y + 2.5 = 0.866025404

Reorder the terms:
2.5 + y = 0.866025404

Solving
2.5 + y = 0.866025404

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 0.866025404 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 0.866025404 + -2.5
y = 0.866025404 + -2.5

Combine like terms: 0.866025404 + -2.5 = -1.633974596
y = -1.633974596

Simplifying
y = -1.633974596

Subproblem 2
y + 2.5 = -0.866025404

Simplifying
y + 2.5 = -0.866025404

Reorder the terms:
2.5 + y = -0.866025404

Solving
2.5 + y = -0.866025404

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -0.866025404 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -0.866025404 + -2.5
y = -0.866025404 + -2.5

Combine like terms: -0.866025404 + -2.5 = -3.366025404
y = -3.366025404

Simplifying
y = -3.366025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.633974596, -3.366025404}