y^2+16y+35=0

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Solution for y^2+16y+35=0 equation: 


Simplifying
y2 + 16y + 35 = 0

Reorder the terms:
35 + 16y + y2 = 0

Solving
35 + 16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 16y + -35 + y2 = 0 + -35

Reorder the terms:
35 + -35 + 16y + y2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 16y + y2 = 0 + -35
16y + y2 = 0 + -35

Combine like terms: 0 + -35 = -35
16y + y2 = -35

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 = -35 + 64

Reorder the terms:
64 + 16y + y2 = -35 + 64

Combine like terms: -35 + 64 = 29
64 + 16y + y2 = 29

Factor a perfect square on the left side:
(y + 8)(y + 8) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(y + 8) equal to 5.385164807 and -5.385164807.


Subproblem 1
y + 8 = 5.385164807

Simplifying
y + 8 = 5.385164807

Reorder the terms:
8 + y = 5.385164807

Solving
8 + y = 5.385164807

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 = 5.385164807 + -8

Combine like terms: 8 + -8 = 0
0 + y = 5.385164807 + -8
y = 5.385164807 + -8

Combine like terms: 5.385164807 + -8 = -2.614835193
y = -2.614835193

Simplifying
y = -2.614835193


Subproblem 2
y + 8 = -5.385164807

Simplifying
y + 8 = -5.385164807

Reorder the terms:
8 + y = -5.385164807

Solving
8 + y = -5.385164807

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 = -5.385164807 + -8

Combine like terms: 8 + -8 = 0
0 + y = -5.385164807 + -8
y = -5.385164807 + -8

Combine like terms: -5.385164807 + -8 = -13.385164807
y = -13.385164807

Simplifying
y = -13.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.614835193, -13.385164807}

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