y^2-6y=2

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Solution for y^2-6y=2 equation: 


Simplifying
y2 + -6y = 2

Reorder the terms:
-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 = 6.31662479
y = 6.31662479

Simplifying
y = 6.31662479


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 = -0.31662479
y = -0.31662479

Simplifying
y = -0.31662479


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

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