0.3y^2+0.15y+-11.7=0

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Solution for 0.3y^2+0.15y+-11.7=0 equation: 


Simplifying
0.3y2 + 0.15y + -11.7 = 0

Reorder the terms:
-11.7 + 0.15y + 0.3y2 = 0

Solving
-11.7 + 0.15y + 0.3y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
0.3 the coefficient of the squared term: 

Divide each side by '0.3'.
-39 + 0.5y + y2 = 0

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + 0.5y + 39 + y2 = 0 + 39

Reorder the terms:
-39 + 39 + 0.5y + y2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + 0.5y + y2 = 0 + 39
0.5y + y2 = 0 + 39

Combine like terms: 0 + 39 = 39
0.5y + y2 = 39

The y term is 0.5y.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5y + 0.0625 + y2 = 39 + 0.0625

Reorder the terms:
0.0625 + 0.5y + y2 = 39 + 0.0625

Combine like terms: 39 + 0.0625 = 39.0625
0.0625 + 0.5y + y2 = 39.0625

Factor a perfect square on the left side:
(y + 0.25)(y + 0.25) = 39.0625

Calculate the square root of the right side: 6.25

Break this problem into two subproblems by setting 
(y + 0.25) equal to 6.25 and -6.25.


Subproblem 1
y + 0.25 = 6.25

Simplifying
y + 0.25 = 6.25

Reorder the terms:
0.25 + y = 6.25

Solving
0.25 + y = 6.25

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = 6.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = 6.25 + -0.25
y = 6.25 + -0.25

Combine like terms: 6.25 + -0.25 = 6
y = 6

Simplifying
y = 6


Subproblem 2
y + 0.25 = -6.25

Simplifying
y + 0.25 = -6.25

Reorder the terms:
0.25 + y = -6.25

Solving
0.25 + y = -6.25

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = -6.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = -6.25 + -0.25
y = -6.25 + -0.25

Combine like terms: -6.25 + -0.25 = -6.5
y = -6.5

Simplifying
y = -6.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6, -6.5}

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