y^2+5.5y=40

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Solution for y^2+5.5y=40 equation: 


Simplifying
y2 + 5.5y = 40

Reorder the terms:
5.5y + y2 = 40

Solving
5.5y + y2 = 40

Solving for variable 'y'.

Reorder the terms:
-40 + 5.5y + y2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 5.5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 5.5y + 40 + y2 = 0 + 40

Reorder the terms:
-40 + 40 + 5.5y + y2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 5.5y + y2 = 0 + 40
5.5y + y2 = 0 + 40

Combine like terms: 0 + 40 = 40
5.5y + y2 = 40

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 = 40 + 7.5625

Reorder the terms:
7.5625 + 5.5y + y2 = 40 + 7.5625

Combine like terms: 40 + 7.5625 = 47.5625
7.5625 + 5.5y + y2 = 47.5625

Factor a perfect square on the left side:
(y + 2.75)(y + 2.75) = 47.5625

Calculate the square root of the right side: 6.896557112

Break this problem into two subproblems by setting 
(y + 2.75) equal to 6.896557112 and -6.896557112.


Subproblem 1
y + 2.75 = 6.896557112

Simplifying
y + 2.75 = 6.896557112

Reorder the terms:
2.75 + y = 6.896557112

Solving
2.75 + y = 6.896557112

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 = 6.896557112 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + y = 6.896557112 + -2.75
y = 6.896557112 + -2.75

Combine like terms: 6.896557112 + -2.75 = 4.146557112
y = 4.146557112

Simplifying
y = 4.146557112


Subproblem 2
y + 2.75 = -6.896557112

Simplifying
y + 2.75 = -6.896557112

Reorder the terms:
2.75 + y = -6.896557112

Solving
2.75 + y = -6.896557112

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 = -6.896557112 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + y = -6.896557112 + -2.75
y = -6.896557112 + -2.75

Combine like terms: -6.896557112 + -2.75 = -9.646557112
y = -9.646557112

Simplifying
y = -9.646557112


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.146557112, -9.646557112}

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