2y^2+8y+5=0

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Solution for 2y^2+8y+5=0 equation: 


Simplifying
2y2 + 8y + 5 = 0

Reorder the terms:
5 + 8y + 2y2 = 0

Solving
5 + 8y + 2y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
2.5 + 4y + y2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 4y + -2.5 + y2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 4y + y2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 4y + y2 = 0 + -2.5
4y + y2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
4y + y2 = -2.5

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = -2.5 + 4

Reorder the terms:
4 + 4y + y2 = -2.5 + 4

Combine like terms: -2.5 + 4 = 1.5
4 + 4y + y2 = 1.5

Factor a perfect square on the left side:
(y + 2)(y + 2) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(y + 2) equal to 1.224744871 and -1.224744871.


Subproblem 1
y + 2 = 1.224744871

Simplifying
y + 2 = 1.224744871

Reorder the terms:
2 + y = 1.224744871

Solving
2 + y = 1.224744871

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = 1.224744871 + -2

Combine like terms: 2 + -2 = 0
0 + y = 1.224744871 + -2
y = 1.224744871 + -2

Combine like terms: 1.224744871 + -2 = -0.775255129
y = -0.775255129

Simplifying
y = -0.775255129


Subproblem 2
y + 2 = -1.224744871

Simplifying
y + 2 = -1.224744871

Reorder the terms:
2 + y = -1.224744871

Solving
2 + y = -1.224744871

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = -1.224744871 + -2

Combine like terms: 2 + -2 = 0
0 + y = -1.224744871 + -2
y = -1.224744871 + -2

Combine like terms: -1.224744871 + -2 = -3.224744871
y = -3.224744871

Simplifying
y = -3.224744871


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.775255129, -3.224744871}

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