y^2+16y-32=0

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Solution for y^2+16y-32=0 equation: 


Simplifying
y2 + 16y + -32 = 0

Reorder the terms:
-32 + 16y + y2 = 0

Solving
-32 + 16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 16y + 32 + y2 = 0 + 32

Reorder the terms:
-32 + 32 + 16y + y2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 16y + y2 = 0 + 32
16y + y2 = 0 + 32

Combine like terms: 0 + 32 = 32
16y + y2 = 32

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 = 32 + 64

Reorder the terms:
64 + 16y + y2 = 32 + 64

Combine like terms: 32 + 64 = 96
64 + 16y + y2 = 96

Factor a perfect square on the left side:
(y + 8)(y + 8) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(y + 8) equal to 9.797958971 and -9.797958971.


Subproblem 1
y + 8 = 9.797958971

Simplifying
y + 8 = 9.797958971

Reorder the terms:
8 + y = 9.797958971

Solving
8 + y = 9.797958971

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 = 9.797958971 + -8

Combine like terms: 8 + -8 = 0
0 + y = 9.797958971 + -8
y = 9.797958971 + -8

Combine like terms: 9.797958971 + -8 = 1.797958971
y = 1.797958971

Simplifying
y = 1.797958971


Subproblem 2
y + 8 = -9.797958971

Simplifying
y + 8 = -9.797958971

Reorder the terms:
8 + y = -9.797958971

Solving
8 + y = -9.797958971

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 = -9.797958971 + -8

Combine like terms: 8 + -8 = 0
0 + y = -9.797958971 + -8
y = -9.797958971 + -8

Combine like terms: -9.797958971 + -8 = -17.797958971
y = -17.797958971

Simplifying
y = -17.797958971


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.797958971, -17.797958971}

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