y^2+19y=0.38

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Solution for y^2+19y=0.38 equation: 


Simplifying
y2 + 19y = 0.38

Reorder the terms:
19y + y2 = 0.38

Solving
19y + y2 = 0.38

Solving for variable 'y'.

Reorder the terms:
-0.38 + 19y + y2 = 0.38 + -0.38

Combine like terms: 0.38 + -0.38 = 0.00
-0.38 + 19y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.38' to each side of the equation.
-0.38 + 19y + 0.38 + y2 = 0.00 + 0.38

Reorder the terms:
-0.38 + 0.38 + 19y + y2 = 0.00 + 0.38

Combine like terms: -0.38 + 0.38 = 0.00
0.00 + 19y + y2 = 0.00 + 0.38
19y + y2 = 0.00 + 0.38

Combine like terms: 0.00 + 0.38 = 0.38
19y + y2 = 0.38

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 = 0.38 + 90.25

Reorder the terms:
90.25 + 19y + y2 = 0.38 + 90.25

Combine like terms: 0.38 + 90.25 = 90.63
90.25 + 19y + y2 = 90.63

Factor a perfect square on the left side:
(y + 9.5)(y + 9.5) = 90.63

Calculate the square root of the right side: 9.519978992

Break this problem into two subproblems by setting 
(y + 9.5) equal to 9.519978992 and -9.519978992.


Subproblem 1
y + 9.5 = 9.519978992

Simplifying
y + 9.5 = 9.519978992

Reorder the terms:
9.5 + y = 9.519978992

Solving
9.5 + y = 9.519978992

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 = 9.519978992 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + y = 9.519978992 + -9.5
y = 9.519978992 + -9.5

Combine like terms: 9.519978992 + -9.5 = 0.019978992
y = 0.019978992

Simplifying
y = 0.019978992


Subproblem 2
y + 9.5 = -9.519978992

Simplifying
y + 9.5 = -9.519978992

Reorder the terms:
9.5 + y = -9.519978992

Solving
9.5 + y = -9.519978992

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 = -9.519978992 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + y = -9.519978992 + -9.5
y = -9.519978992 + -9.5

Combine like terms: -9.519978992 + -9.5 = -19.019978992
y = -19.019978992

Simplifying
y = -19.019978992


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.019978992, -19.019978992}

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