y^2+8y-32=0

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Solution for y^2+8y-32=0 equation: 


Simplifying
y2 + 8y + -32 = 0

Reorder the terms:
-32 + 8y + y2 = 0

Solving
-32 + 8y + 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 + 8y + 32 + y2 = 0 + 32

Reorder the terms:
-32 + 32 + 8y + y2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 8y + y2 = 0 + 32
8y + y2 = 0 + 32

Combine like terms: 0 + 32 = 32
8y + y2 = 32

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 32 + 16

Reorder the terms:
16 + 8y + y2 = 32 + 16

Combine like terms: 32 + 16 = 48
16 + 8y + y2 = 48

Factor a perfect square on the left side:
(y + 4)(y + 4) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(y + 4) equal to 6.92820323 and -6.92820323.


Subproblem 1
y + 4 = 6.92820323

Simplifying
y + 4 = 6.92820323

Reorder the terms:
4 + y = 6.92820323

Solving
4 + y = 6.92820323

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + y = 6.92820323 + -4

Combine like terms: 4 + -4 = 0
0 + y = 6.92820323 + -4
y = 6.92820323 + -4

Combine like terms: 6.92820323 + -4 = 2.92820323
y = 2.92820323

Simplifying
y = 2.92820323


Subproblem 2
y + 4 = -6.92820323

Simplifying
y + 4 = -6.92820323

Reorder the terms:
4 + y = -6.92820323

Solving
4 + y = -6.92820323

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + y = -6.92820323 + -4

Combine like terms: 4 + -4 = 0
0 + y = -6.92820323 + -4
y = -6.92820323 + -4

Combine like terms: -6.92820323 + -4 = -10.92820323
y = -10.92820323

Simplifying
y = -10.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.92820323, -10.92820323}

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