y^2+16y=2

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


Simplifying
y2 + 16y = 2

Reorder the terms:
16y + y2 = 2

Solving
16y + y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + 16y + y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 16y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 16y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 16y + y2 = 0 + 2
16y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
16y + y2 = 2

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 = 2 + 64

Reorder the terms:
64 + 16y + y2 = 2 + 64

Combine like terms: 2 + 64 = 66
64 + 16y + y2 = 66

Factor a perfect square on the left side:
(y + 8)(y + 8) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(y + 8) equal to 8.124038405 and -8.124038405.


Subproblem 1
y + 8 = 8.124038405

Simplifying
y + 8 = 8.124038405

Reorder the terms:
8 + y = 8.124038405

Solving
8 + y = 8.124038405

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 = 8.124038405 + -8

Combine like terms: 8 + -8 = 0
0 + y = 8.124038405 + -8
y = 8.124038405 + -8

Combine like terms: 8.124038405 + -8 = 0.124038405
y = 0.124038405

Simplifying
y = 0.124038405


Subproblem 2
y + 8 = -8.124038405

Simplifying
y + 8 = -8.124038405

Reorder the terms:
8 + y = -8.124038405

Solving
8 + y = -8.124038405

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 = -8.124038405 + -8

Combine like terms: 8 + -8 = 0
0 + y = -8.124038405 + -8
y = -8.124038405 + -8

Combine like terms: -8.124038405 + -8 = -16.124038405
y = -16.124038405

Simplifying
y = -16.124038405


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.124038405, -16.124038405}

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