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 = 14.25
30.25 + 11y + y2 = 14.25

Factor a perfect square on the left side:
(y + 5.5)(y + 5.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(y + 5.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
y + 5.5 = 3.774917218

Simplifying
y + 5.5 = 3.774917218

Reorder the terms:
5.5 + y = 3.774917218

Solving
5.5 + y = 3.774917218

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 = 3.774917218 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + y = 3.774917218 + -5.5
y = 3.774917218 + -5.5

Combine like terms: 3.774917218 + -5.5 = -1.725082782
y = -1.725082782

Simplifying
y = -1.725082782


Subproblem 2
y + 5.5 = -3.774917218

Simplifying
y + 5.5 = -3.774917218

Reorder the terms:
5.5 + y = -3.774917218

Solving
5.5 + y = -3.774917218

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 = -3.774917218 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + y = -3.774917218 + -5.5
y = -3.774917218 + -5.5

Combine like terms: -3.774917218 + -5.5 = -9.274917218
y = -9.274917218

Simplifying
y = -9.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.725082782, -9.274917218}

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