y^2+20y+40=0

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Solution for y^2+20y+40=0 equation: 


Simplifying
y2 + 20y + 40 = 0

Reorder the terms:
40 + 20y + y2 = 0

Solving
40 + 20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 20y + -40 + y2 = 0 + -40

Reorder the terms:
40 + -40 + 20y + y2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 20y + y2 = 0 + -40
20y + y2 = 0 + -40

Combine like terms: 0 + -40 = -40
20y + y2 = -40

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 = -40 + 100

Reorder the terms:
100 + 20y + y2 = -40 + 100

Combine like terms: -40 + 100 = 60
100 + 20y + y2 = 60

Factor a perfect square on the left side:
(y + 10)(y + 10) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(y + 10) equal to 7.745966692 and -7.745966692.


Subproblem 1
y + 10 = 7.745966692

Simplifying
y + 10 = 7.745966692

Reorder the terms:
10 + y = 7.745966692

Solving
10 + y = 7.745966692

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 = 7.745966692 + -10

Combine like terms: 10 + -10 = 0
0 + y = 7.745966692 + -10
y = 7.745966692 + -10

Combine like terms: 7.745966692 + -10 = -2.254033308
y = -2.254033308

Simplifying
y = -2.254033308


Subproblem 2
y + 10 = -7.745966692

Simplifying
y + 10 = -7.745966692

Reorder the terms:
10 + y = -7.745966692

Solving
10 + y = -7.745966692

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 = -7.745966692 + -10

Combine like terms: 10 + -10 = 0
0 + y = -7.745966692 + -10
y = -7.745966692 + -10

Combine like terms: -7.745966692 + -10 = -17.745966692
y = -17.745966692

Simplifying
y = -17.745966692


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.254033308, -17.745966692}

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