y^2-22y-100=0

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Solution for y^2-22y-100=0 equation: 


Simplifying
y2 + -22y + -100 = 0

Reorder the terms:
-100 + -22y + y2 = 0

Solving
-100 + -22y + 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 + -22y + 100 + y2 = 0 + 100

Reorder the terms:
-100 + 100 + -22y + y2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -22y + y2 = 0 + 100
-22y + y2 = 0 + 100

Combine like terms: 0 + 100 = 100
-22y + y2 = 100

The y term is -22y.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22y + 121 + y2 = 100 + 121

Reorder the terms:
121 + -22y + y2 = 100 + 121

Combine like terms: 100 + 121 = 221
121 + -22y + y2 = 221

Factor a perfect square on the left side:
(y + -11)(y + -11) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(y + -11) equal to 14.866068747 and -14.866068747.


Subproblem 1
y + -11 = 14.866068747

Simplifying
y + -11 = 14.866068747

Reorder the terms:
-11 + y = 14.866068747

Solving
-11 + y = 14.866068747

Solving for variable 'y'.

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

Add '11' to each side of the equation.
-11 + 11 + y = 14.866068747 + 11

Combine like terms: -11 + 11 = 0
0 + y = 14.866068747 + 11
y = 14.866068747 + 11

Combine like terms: 14.866068747 + 11 = 25.866068747
y = 25.866068747

Simplifying
y = 25.866068747


Subproblem 2
y + -11 = -14.866068747

Simplifying
y + -11 = -14.866068747

Reorder the terms:
-11 + y = -14.866068747

Solving
-11 + y = -14.866068747

Solving for variable 'y'.

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

Add '11' to each side of the equation.
-11 + 11 + y = -14.866068747 + 11

Combine like terms: -11 + 11 = 0
0 + y = -14.866068747 + 11
y = -14.866068747 + 11

Combine like terms: -14.866068747 + 11 = -3.866068747
y = -3.866068747

Simplifying
y = -3.866068747


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {25.866068747, -3.866068747}

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