y^2+18y+41=0

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Solution for y^2+18y+41=0 equation: 


Simplifying
y2 + 18y + 41 = 0

Reorder the terms:
41 + 18y + y2 = 0

Solving
41 + 18y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + 18y + -41 + y2 = 0 + -41

Reorder the terms:
41 + -41 + 18y + y2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 18y + y2 = 0 + -41
18y + y2 = 0 + -41

Combine like terms: 0 + -41 = -41
18y + y2 = -41

The y term is 18y.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18y + 81 + y2 = -41 + 81

Reorder the terms:
81 + 18y + y2 = -41 + 81

Combine like terms: -41 + 81 = 40
81 + 18y + y2 = 40

Factor a perfect square on the left side:
(y + 9)(y + 9) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(y + 9) equal to 6.32455532 and -6.32455532.


Subproblem 1
y + 9 = 6.32455532

Simplifying
y + 9 = 6.32455532

Reorder the terms:
9 + y = 6.32455532

Solving
9 + y = 6.32455532

Solving for variable 'y'.

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

Add '-9' to each side of the equation.
9 + -9 + y = 6.32455532 + -9

Combine like terms: 9 + -9 = 0
0 + y = 6.32455532 + -9
y = 6.32455532 + -9

Combine like terms: 6.32455532 + -9 = -2.67544468
y = -2.67544468

Simplifying
y = -2.67544468


Subproblem 2
y + 9 = -6.32455532

Simplifying
y + 9 = -6.32455532

Reorder the terms:
9 + y = -6.32455532

Solving
9 + y = -6.32455532

Solving for variable 'y'.

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

Add '-9' to each side of the equation.
9 + -9 + y = -6.32455532 + -9

Combine like terms: 9 + -9 = 0
0 + y = -6.32455532 + -9
y = -6.32455532 + -9

Combine like terms: -6.32455532 + -9 = -15.32455532
y = -15.32455532

Simplifying
y = -15.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.67544468, -15.32455532}

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