y^2-16y+8=0

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Solution for y^2-16y+8=0 equation: 


Simplifying
y2 + -16y + 8 = 0

Reorder the terms:
8 + -16y + y2 = 0

Solving
8 + -16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -16y + -8 + y2 = 0 + -8

Reorder the terms:
8 + -8 + -16y + y2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -16y + y2 = 0 + -8
-16y + y2 = 0 + -8

Combine like terms: 0 + -8 = -8
-16y + y2 = -8

The y term is -16y.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16y + 64 + y2 = -8 + 64

Reorder the terms:
64 + -16y + y2 = -8 + 64

Combine like terms: -8 + 64 = 56
64 + -16y + y2 = 56

Factor a perfect square on the left side:
(y + -8)(y + -8) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(y + -8) equal to 7.483314774 and -7.483314774.


Subproblem 1
y + -8 = 7.483314774

Simplifying
y + -8 = 7.483314774

Reorder the terms:
-8 + y = 7.483314774

Solving
-8 + y = 7.483314774

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = 7.483314774 + 8

Combine like terms: -8 + 8 = 0
0 + y = 7.483314774 + 8
y = 7.483314774 + 8

Combine like terms: 7.483314774 + 8 = 15.483314774
y = 15.483314774

Simplifying
y = 15.483314774


Subproblem 2
y + -8 = -7.483314774

Simplifying
y + -8 = -7.483314774

Reorder the terms:
-8 + y = -7.483314774

Solving
-8 + y = -7.483314774

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = -7.483314774 + 8

Combine like terms: -8 + 8 = 0
0 + y = -7.483314774 + 8
y = -7.483314774 + 8

Combine like terms: -7.483314774 + 8 = 0.516685226
y = 0.516685226

Simplifying
y = 0.516685226


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {15.483314774, 0.516685226}

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