y^2+20y+30=0

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Solution for y^2+20y+30=0 equation: 


Simplifying
y2 + 20y + 30 = 0

Reorder the terms:
30 + 20y + y2 = 0

Solving
30 + 20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 20y + -30 + y2 = 0 + -30

Reorder the terms:
30 + -30 + 20y + y2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 20y + y2 = 0 + -30
20y + y2 = 0 + -30

Combine like terms: 0 + -30 = -30
20y + y2 = -30

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 = -30 + 100

Reorder the terms:
100 + 20y + y2 = -30 + 100

Combine like terms: -30 + 100 = 70
100 + 20y + y2 = 70

Factor a perfect square on the left side:
(y + 10)(y + 10) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(y + 10) equal to 8.366600265 and -8.366600265.


Subproblem 1
y + 10 = 8.366600265

Simplifying
y + 10 = 8.366600265

Reorder the terms:
10 + y = 8.366600265

Solving
10 + y = 8.366600265

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 = 8.366600265 + -10

Combine like terms: 10 + -10 = 0
0 + y = 8.366600265 + -10
y = 8.366600265 + -10

Combine like terms: 8.366600265 + -10 = -1.633399735
y = -1.633399735

Simplifying
y = -1.633399735


Subproblem 2
y + 10 = -8.366600265

Simplifying
y + 10 = -8.366600265

Reorder the terms:
10 + y = -8.366600265

Solving
10 + y = -8.366600265

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 = -8.366600265 + -10

Combine like terms: 10 + -10 = 0
0 + y = -8.366600265 + -10
y = -8.366600265 + -10

Combine like terms: -8.366600265 + -10 = -18.366600265
y = -18.366600265

Simplifying
y = -18.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.633399735, -18.366600265}

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