y(y+6)=2

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Solution for y(y+6)=2 equation: 


Simplifying
y(y + 6) = 2

Reorder the terms:
y(6 + y) = 2
(6 * y + y * y) = 2
(6y + y2) = 2

Solving
6y + y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + 6y + y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 6y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6y + y2 = 0 + 2
6y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
6y + y2 = 2

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 2 + 9

Reorder the terms:
9 + 6y + y2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + 6y + y2 = 11

Factor a perfect square on the left side:
(y + 3)(y + 3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(y + 3) equal to 3.31662479 and -3.31662479.


Subproblem 1
y + 3 = 3.31662479

Simplifying
y + 3 = 3.31662479

Reorder the terms:
3 + y = 3.31662479

Solving
3 + y = 3.31662479

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 3.31662479 + -3

Combine like terms: 3 + -3 = 0
0 + y = 3.31662479 + -3
y = 3.31662479 + -3

Combine like terms: 3.31662479 + -3 = 0.31662479
y = 0.31662479

Simplifying
y = 0.31662479


Subproblem 2
y + 3 = -3.31662479

Simplifying
y + 3 = -3.31662479

Reorder the terms:
3 + y = -3.31662479

Solving
3 + y = -3.31662479

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -3.31662479 + -3

Combine like terms: 3 + -3 = 0
0 + y = -3.31662479 + -3
y = -3.31662479 + -3

Combine like terms: -3.31662479 + -3 = -6.31662479
y = -6.31662479

Simplifying
y = -6.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.31662479, -6.31662479}

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