y^2-11y-16=0

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Solution for y^2-11y-16=0 equation: 


Simplifying
y2 + -11y + -16 = 0

Reorder the terms:
-16 + -11y + y2 = 0

Solving
-16 + -11y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -11y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + -11y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -11y + y2 = 0 + 16
-11y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
-11y + y2 = 16

The y term is -11y.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11y + 30.25 + y2 = 16 + 30.25

Reorder the terms:
30.25 + -11y + y2 = 16 + 30.25

Combine like terms: 16 + 30.25 = 46.25
30.25 + -11y + y2 = 46.25

Factor a perfect square on the left side:
(y + -5.5)(y + -5.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(y + -5.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
y + -5.5 = 6.800735254

Simplifying
y + -5.5 = 6.800735254

Reorder the terms:
-5.5 + y = 6.800735254

Solving
-5.5 + y = 6.800735254

Solving for variable 'y'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + y = 6.800735254 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = 6.800735254 + 5.5
y = 6.800735254 + 5.5

Combine like terms: 6.800735254 + 5.5 = 12.300735254
y = 12.300735254

Simplifying
y = 12.300735254


Subproblem 2
y + -5.5 = -6.800735254

Simplifying
y + -5.5 = -6.800735254

Reorder the terms:
-5.5 + y = -6.800735254

Solving
-5.5 + y = -6.800735254

Solving for variable 'y'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + y = -6.800735254 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = -6.800735254 + 5.5
y = -6.800735254 + 5.5

Combine like terms: -6.800735254 + 5.5 = -1.300735254
y = -1.300735254

Simplifying
y = -1.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.300735254, -1.300735254}

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