4y^2+36y+8=0

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Solution for 4y^2+36y+8=0 equation: 


Simplifying
4y2 + 36y + 8 = 0

Reorder the terms:
8 + 36y + 4y2 = 0

Solving
8 + 36y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 9y + y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + 9y + y2)' equal to zero and attempt to solve:

Simplifying
2 + 9y + y2 = 0

Solving
2 + 9y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 9y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 9y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9y + y2 = 0 + -2
9y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
9y + y2 = -2

The y term is 9y.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9y + 20.25 + y2 = -2 + 20.25

Reorder the terms:
20.25 + 9y + y2 = -2 + 20.25

Combine like terms: -2 + 20.25 = 18.25
20.25 + 9y + y2 = 18.25

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(y + 4.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
y + 4.5 = 4.272001873

Simplifying
y + 4.5 = 4.272001873

Reorder the terms:
4.5 + y = 4.272001873

Solving
4.5 + y = 4.272001873

Solving for variable 'y'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = 4.272001873 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = 4.272001873 + -4.5
y = 4.272001873 + -4.5

Combine like terms: 4.272001873 + -4.5 = -0.227998127
y = -0.227998127

Simplifying
y = -0.227998127


Subproblem 2
y + 4.5 = -4.272001873

Simplifying
y + 4.5 = -4.272001873

Reorder the terms:
4.5 + y = -4.272001873

Solving
4.5 + y = -4.272001873

Solving for variable 'y'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = -4.272001873 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = -4.272001873 + -4.5
y = -4.272001873 + -4.5

Combine like terms: -4.272001873 + -4.5 = -8.772001873
y = -8.772001873

Simplifying
y = -8.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.227998127, -8.772001873}
Solution
y = {-0.227998127, -8.772001873}

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