y^2-16y-100=0

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Solution for y^2-16y-100=0 equation: 


Simplifying
y2 + -16y + -100 = 0

Reorder the terms:
-100 + -16y + y2 = 0

Solving
-100 + -16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -16y + 100 + y2 = 0 + 100

Reorder the terms:
-100 + 100 + -16y + y2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -16y + y2 = 0 + 100
-16y + y2 = 0 + 100

Combine like terms: 0 + 100 = 100
-16y + y2 = 100

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 = 100 + 64

Reorder the terms:
64 + -16y + y2 = 100 + 64

Combine like terms: 100 + 64 = 164
64 + -16y + y2 = 164

Factor a perfect square on the left side:
(y + -8)(y + -8) = 164

Calculate the square root of the right side: 12.806248475

Break this problem into two subproblems by setting 
(y + -8) equal to 12.806248475 and -12.806248475.


Subproblem 1
y + -8 = 12.806248475

Simplifying
y + -8 = 12.806248475

Reorder the terms:
-8 + y = 12.806248475

Solving
-8 + y = 12.806248475

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 = 12.806248475 + 8

Combine like terms: -8 + 8 = 0
0 + y = 12.806248475 + 8
y = 12.806248475 + 8

Combine like terms: 12.806248475 + 8 = 20.806248475
y = 20.806248475

Simplifying
y = 20.806248475


Subproblem 2
y + -8 = -12.806248475

Simplifying
y + -8 = -12.806248475

Reorder the terms:
-8 + y = -12.806248475

Solving
-8 + y = -12.806248475

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 = -12.806248475 + 8

Combine like terms: -8 + 8 = 0
0 + y = -12.806248475 + 8
y = -12.806248475 + 8

Combine like terms: -12.806248475 + 8 = -4.806248475
y = -4.806248475

Simplifying
y = -4.806248475


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {20.806248475, -4.806248475}

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