8.666666667+y=y^2

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Solution for 8.666666667+y=y^2 equation: 


Simplifying
8.666666667 + y = y2

Solving
8.666666667 + y = y2

Solving for variable 'y'.

Combine like terms: y2 + -1y2 = 0
8.666666667 + y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8.666666667 + -1y + y2 = 0

Move the constant term to the right:

Add '8.666666667' to each side of the equation.
-8.666666667 + -1y + 8.666666667 + y2 = 0 + 8.666666667

Reorder the terms:
-8.666666667 + 8.666666667 + -1y + y2 = 0 + 8.666666667

Combine like terms: -8.666666667 + 8.666666667 = 0.000000000
0.000000000 + -1y + y2 = 0 + 8.666666667
-1y + y2 = 0 + 8.666666667

Combine like terms: 0 + 8.666666667 = 8.666666667
-1y + y2 = 8.666666667

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.
-1y + 0.25 + y2 = 8.666666667 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 8.666666667 + 0.25

Combine like terms: 8.666666667 + 0.25 = 8.916666667
0.25 + -1y + y2 = 8.916666667

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 8.916666667

Calculate the square root of the right side: 2.986078811

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.986078811 and -2.986078811.


Subproblem 1
y + 0.5 = 2.986078811

Simplifying
y + 0.5 = 2.986078811

Reorder the terms:
0.5 + y = 2.986078811

Solving
0.5 + y = 2.986078811

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 = 2.986078811 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.986078811 + -0.5
y = 2.986078811 + -0.5

Combine like terms: 2.986078811 + -0.5 = 2.486078811
y = 2.486078811

Simplifying
y = 2.486078811


Subproblem 2
y + 0.5 = -2.986078811

Simplifying
y + 0.5 = -2.986078811

Reorder the terms:
0.5 + y = -2.986078811

Solving
0.5 + y = -2.986078811

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 = -2.986078811 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.986078811 + -0.5
y = -2.986078811 + -0.5

Combine like terms: -2.986078811 + -0.5 = -3.486078811
y = -3.486078811

Simplifying
y = -3.486078811


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.486078811, -3.486078811}

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