Y^2+19Y+6=0

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Solution for Y^2+19Y+6=0 equation: 


Simplifying
Y2 + 19Y + 6 = 0

Reorder the terms:
6 + 19Y + Y2 = 0

Solving
6 + 19Y + Y2 = 0

Solving for variable 'Y'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 19Y + -6 + Y2 = 0 + -6

Reorder the terms:
6 + -6 + 19Y + Y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 19Y + Y2 = 0 + -6
19Y + Y2 = 0 + -6

Combine like terms: 0 + -6 = -6
19Y + Y2 = -6

The Y term is 19Y.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19Y + 90.25 + Y2 = -6 + 90.25

Reorder the terms:
90.25 + 19Y + Y2 = -6 + 90.25

Combine like terms: -6 + 90.25 = 84.25
90.25 + 19Y + Y2 = 84.25

Factor a perfect square on the left side:
(Y + 9.5)(Y + 9.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(Y + 9.5) equal to 9.178779875 and -9.178779875.


Subproblem 1
Y + 9.5 = 9.178779875

Simplifying
Y + 9.5 = 9.178779875

Reorder the terms:
9.5 + Y = 9.178779875

Solving
9.5 + Y = 9.178779875

Solving for variable 'Y'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + Y = 9.178779875 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + Y = 9.178779875 + -9.5
Y = 9.178779875 + -9.5

Combine like terms: 9.178779875 + -9.5 = -0.321220125
Y = -0.321220125

Simplifying
Y = -0.321220125


Subproblem 2
Y + 9.5 = -9.178779875

Simplifying
Y + 9.5 = -9.178779875

Reorder the terms:
9.5 + Y = -9.178779875

Solving
9.5 + Y = -9.178779875

Solving for variable 'Y'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + Y = -9.178779875 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + Y = -9.178779875 + -9.5
Y = -9.178779875 + -9.5

Combine like terms: -9.178779875 + -9.5 = -18.678779875
Y = -18.678779875

Simplifying
Y = -18.678779875


Solution
The solution to the problem is based on the solutions
from the subproblems.
Y = {-0.321220125, -18.678779875}

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