2y^2+2y-11=0

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


Simplifying
2y2 + 2y + -11 = 0

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

Solving
-11 + 2y + 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 + y + y2 = 0

Move the constant term to the right:

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

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

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

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

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + y2 = 5.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 5.5 + 0.25

Combine like terms: 5.5 + 0.25 = 5.75
1.25 + y2 = 5.75

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.397915762 and -2.397915762.


Subproblem 1
y + 0.5 = 2.397915762

Simplifying
y + 0.5 = 2.397915762

Reorder the terms:
0.5 + y = 2.397915762

Solving
0.5 + y = 2.397915762

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 2.397915762 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.397915762 + -0.5
y = 2.397915762 + -0.5

Combine like terms: 2.397915762 + -0.5 = 1.897915762
y = 1.897915762

Simplifying
y = 1.897915762


Subproblem 2
y + 0.5 = -2.397915762

Simplifying
y + 0.5 = -2.397915762

Reorder the terms:
0.5 + y = -2.397915762

Solving
0.5 + y = -2.397915762

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -2.397915762 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.397915762 + -0.5
y = -2.397915762 + -0.5

Combine like terms: -2.397915762 + -0.5 = -2.897915762
y = -2.897915762

Simplifying
y = -2.897915762


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.897915762, -2.897915762}

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