y^2-16y+32=0

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Solution for y^2-16y+32=0 equation: 


Simplifying
y2 + -16y + 32 = 0

Reorder the terms:
32 + -16y + y2 = 0

Solving
32 + -16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -16y + -32 + y2 = 0 + -32

Reorder the terms:
32 + -32 + -16y + y2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -16y + y2 = 0 + -32
-16y + y2 = 0 + -32

Combine like terms: 0 + -32 = -32
-16y + y2 = -32

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 = -32 + 64

Reorder the terms:
64 + -16y + y2 = -32 + 64

Combine like terms: -32 + 64 = 32
64 + -16y + y2 = 32

Factor a perfect square on the left side:
(y + -8)(y + -8) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(y + -8) equal to 5.656854249 and -5.656854249.


Subproblem 1
y + -8 = 5.656854249

Simplifying
y + -8 = 5.656854249

Reorder the terms:
-8 + y = 5.656854249

Solving
-8 + y = 5.656854249

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 = 5.656854249 + 8

Combine like terms: -8 + 8 = 0
0 + y = 5.656854249 + 8
y = 5.656854249 + 8

Combine like terms: 5.656854249 + 8 = 13.656854249
y = 13.656854249

Simplifying
y = 13.656854249


Subproblem 2
y + -8 = -5.656854249

Simplifying
y + -8 = -5.656854249

Reorder the terms:
-8 + y = -5.656854249

Solving
-8 + y = -5.656854249

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 = -5.656854249 + 8

Combine like terms: -8 + 8 = 0
0 + y = -5.656854249 + 8
y = -5.656854249 + 8

Combine like terms: -5.656854249 + 8 = 2.343145751
y = 2.343145751

Simplifying
y = 2.343145751


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {13.656854249, 2.343145751}

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