y^2+16y+64=5

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Solution for y^2+16y+64=5 equation: 


Simplifying
y2 + 16y + 64 = 5

Reorder the terms:
64 + 16y + y2 = 5

Solving
64 + 16y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
64 + -5 + 16y + y2 = 5 + -5

Combine like terms: 64 + -5 = 59
59 + 16y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
59 + 16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-59' to each side of the equation.
59 + 16y + -59 + y2 = 0 + -59

Reorder the terms:
59 + -59 + 16y + y2 = 0 + -59

Combine like terms: 59 + -59 = 0
0 + 16y + y2 = 0 + -59
16y + y2 = 0 + -59

Combine like terms: 0 + -59 = -59
16y + y2 = -59

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 = -59 + 64

Reorder the terms:
64 + 16y + y2 = -59 + 64

Combine like terms: -59 + 64 = 5
64 + 16y + y2 = 5

Factor a perfect square on the left side:
(y + 8)(y + 8) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(y + 8) equal to 2.236067978 and -2.236067978.


Subproblem 1
y + 8 = 2.236067978

Simplifying
y + 8 = 2.236067978

Reorder the terms:
8 + y = 2.236067978

Solving
8 + y = 2.236067978

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 = 2.236067978 + -8

Combine like terms: 8 + -8 = 0
0 + y = 2.236067978 + -8
y = 2.236067978 + -8

Combine like terms: 2.236067978 + -8 = -5.763932022
y = -5.763932022

Simplifying
y = -5.763932022


Subproblem 2
y + 8 = -2.236067978

Simplifying
y + 8 = -2.236067978

Reorder the terms:
8 + y = -2.236067978

Solving
8 + y = -2.236067978

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 = -2.236067978 + -8

Combine like terms: 8 + -8 = 0
0 + y = -2.236067978 + -8
y = -2.236067978 + -8

Combine like terms: -2.236067978 + -8 = -10.236067978
y = -10.236067978

Simplifying
y = -10.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-5.763932022, -10.236067978}

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