y^2+16y+16=0

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


Simplifying
y2 + 16y + 16 = 0

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

Solving
16 + 16y + 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 + 16y + -16 + y2 = 0 + -16

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

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

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

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 = -16 + 64

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

Combine like terms: -16 + 64 = 48
64 + 16y + y2 = 48

Factor a perfect square on the left side:
(y + 8)(y + 8) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(y + 8) equal to 6.92820323 and -6.92820323.


Subproblem 1
y + 8 = 6.92820323

Simplifying
y + 8 = 6.92820323

Reorder the terms:
8 + y = 6.92820323

Solving
8 + y = 6.92820323

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 = 6.92820323 + -8

Combine like terms: 8 + -8 = 0
0 + y = 6.92820323 + -8
y = 6.92820323 + -8

Combine like terms: 6.92820323 + -8 = -1.07179677
y = -1.07179677

Simplifying
y = -1.07179677


Subproblem 2
y + 8 = -6.92820323

Simplifying
y + 8 = -6.92820323

Reorder the terms:
8 + y = -6.92820323

Solving
8 + y = -6.92820323

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 = -6.92820323 + -8

Combine like terms: 8 + -8 = 0
0 + y = -6.92820323 + -8
y = -6.92820323 + -8

Combine like terms: -6.92820323 + -8 = -14.92820323
y = -14.92820323

Simplifying
y = -14.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.07179677, -14.92820323}

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