y^2+20y+20=0

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Solution for y^2+20y+20=0 equation: 


Simplifying
y2 + 20y + 20 = 0

Reorder the terms:
20 + 20y + y2 = 0

Solving
20 + 20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 20y + -20 + y2 = 0 + -20

Reorder the terms:
20 + -20 + 20y + y2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 20y + y2 = 0 + -20
20y + y2 = 0 + -20

Combine like terms: 0 + -20 = -20
20y + y2 = -20

The y term is 20y.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20y + 100 + y2 = -20 + 100

Reorder the terms:
100 + 20y + y2 = -20 + 100

Combine like terms: -20 + 100 = 80
100 + 20y + y2 = 80

Factor a perfect square on the left side:
(y + 10)(y + 10) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(y + 10) equal to 8.94427191 and -8.94427191.


Subproblem 1
y + 10 = 8.94427191

Simplifying
y + 10 = 8.94427191

Reorder the terms:
10 + y = 8.94427191

Solving
10 + y = 8.94427191

Solving for variable 'y'.

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

Add '-10' to each side of the equation.
10 + -10 + y = 8.94427191 + -10

Combine like terms: 10 + -10 = 0
0 + y = 8.94427191 + -10
y = 8.94427191 + -10

Combine like terms: 8.94427191 + -10 = -1.05572809
y = -1.05572809

Simplifying
y = -1.05572809


Subproblem 2
y + 10 = -8.94427191

Simplifying
y + 10 = -8.94427191

Reorder the terms:
10 + y = -8.94427191

Solving
10 + y = -8.94427191

Solving for variable 'y'.

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

Add '-10' to each side of the equation.
10 + -10 + y = -8.94427191 + -10

Combine like terms: 10 + -10 = 0
0 + y = -8.94427191 + -10
y = -8.94427191 + -10

Combine like terms: -8.94427191 + -10 = -18.94427191
y = -18.94427191

Simplifying
y = -18.94427191


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.05572809, -18.94427191}

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