y^2-8y=2

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Solution for y^2-8y=2 equation: 


Simplifying
y2 + -8y = 2

Reorder the terms:
-8y + y2 = 2

Solving
-8y + y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + -8y + y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + -8y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -8y + y2 = 0 + 2
-8y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-8y + y2 = 2

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = 2 + 16

Reorder the terms:
16 + -8y + y2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + -8y + y2 = 18

Factor a perfect square on the left side:
(y + -4)(y + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(y + -4) equal to 4.242640687 and -4.242640687.


Subproblem 1
y + -4 = 4.242640687

Simplifying
y + -4 = 4.242640687

Reorder the terms:
-4 + y = 4.242640687

Solving
-4 + y = 4.242640687

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + y = 4.242640687 + 4
y = 4.242640687 + 4

Combine like terms: 4.242640687 + 4 = 8.242640687
y = 8.242640687

Simplifying
y = 8.242640687


Subproblem 2
y + -4 = -4.242640687

Simplifying
y + -4 = -4.242640687

Reorder the terms:
-4 + y = -4.242640687

Solving
-4 + y = -4.242640687

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + y = -4.242640687 + 4
y = -4.242640687 + 4

Combine like terms: -4.242640687 + 4 = -0.242640687
y = -0.242640687

Simplifying
y = -0.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.242640687, -0.242640687}

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