y^2+36y+32=0

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Solution for y^2+36y+32=0 equation: 


Simplifying
y2 + 36y + 32 = 0

Reorder the terms:
32 + 36y + y2 = 0

Solving
32 + 36y + 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 + 36y + -32 + y2 = 0 + -32

Reorder the terms:
32 + -32 + 36y + y2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 36y + y2 = 0 + -32
36y + y2 = 0 + -32

Combine like terms: 0 + -32 = -32
36y + y2 = -32

The y term is 36y.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36y + 324 + y2 = -32 + 324

Reorder the terms:
324 + 36y + y2 = -32 + 324

Combine like terms: -32 + 324 = 292
324 + 36y + y2 = 292

Factor a perfect square on the left side:
(y + 18)(y + 18) = 292

Calculate the square root of the right side: 17.088007491

Break this problem into two subproblems by setting 
(y + 18) equal to 17.088007491 and -17.088007491.


Subproblem 1
y + 18 = 17.088007491

Simplifying
y + 18 = 17.088007491

Reorder the terms:
18 + y = 17.088007491

Solving
18 + y = 17.088007491

Solving for variable 'y'.

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

Add '-18' to each side of the equation.
18 + -18 + y = 17.088007491 + -18

Combine like terms: 18 + -18 = 0
0 + y = 17.088007491 + -18
y = 17.088007491 + -18

Combine like terms: 17.088007491 + -18 = -0.911992509
y = -0.911992509

Simplifying
y = -0.911992509


Subproblem 2
y + 18 = -17.088007491

Simplifying
y + 18 = -17.088007491

Reorder the terms:
18 + y = -17.088007491

Solving
18 + y = -17.088007491

Solving for variable 'y'.

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

Add '-18' to each side of the equation.
18 + -18 + y = -17.088007491 + -18

Combine like terms: 18 + -18 = 0
0 + y = -17.088007491 + -18
y = -17.088007491 + -18

Combine like terms: -17.088007491 + -18 = -35.088007491
y = -35.088007491

Simplifying
y = -35.088007491


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.911992509, -35.088007491}

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