9y^2+30y+17=0

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Solution for 9y^2+30y+17=0 equation: 


Simplifying
9y2 + 30y + 17 = 0

Reorder the terms:
17 + 30y + 9y2 = 0

Solving
17 + 30y + 9y2 = 0

Solving for variable 'y'.

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

Divide each side by '9'.
1.888888889 + 3.333333333y + y2 = 0

Move the constant term to the right:

Add '-1.888888889' to each side of the equation.
1.888888889 + 3.333333333y + -1.888888889 + y2 = 0 + -1.888888889

Reorder the terms:
1.888888889 + -1.888888889 + 3.333333333y + y2 = 0 + -1.888888889

Combine like terms: 1.888888889 + -1.888888889 = 0.000000000
0.000000000 + 3.333333333y + y2 = 0 + -1.888888889
3.333333333y + y2 = 0 + -1.888888889

Combine like terms: 0 + -1.888888889 = -1.888888889
3.333333333y + y2 = -1.888888889

The y term is 3.333333333y.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333y + 2.777777779 + y2 = -1.888888889 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333y + y2 = -1.888888889 + 2.777777779

Combine like terms: -1.888888889 + 2.777777779 = 0.88888889
2.777777779 + 3.333333333y + y2 = 0.88888889

Factor a perfect square on the left side:
(y + 1.666666667)(y + 1.666666667) = 0.88888889

Calculate the square root of the right side: 0.942809042

Break this problem into two subproblems by setting 
(y + 1.666666667) equal to 0.942809042 and -0.942809042.


Subproblem 1
y + 1.666666667 = 0.942809042

Simplifying
y + 1.666666667 = 0.942809042

Reorder the terms:
1.666666667 + y = 0.942809042

Solving
1.666666667 + y = 0.942809042

Solving for variable 'y'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + y = 0.942809042 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + y = 0.942809042 + -1.666666667
y = 0.942809042 + -1.666666667

Combine like terms: 0.942809042 + -1.666666667 = -0.723857625
y = -0.723857625

Simplifying
y = -0.723857625


Subproblem 2
y + 1.666666667 = -0.942809042

Simplifying
y + 1.666666667 = -0.942809042

Reorder the terms:
1.666666667 + y = -0.942809042

Solving
1.666666667 + y = -0.942809042

Solving for variable 'y'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + y = -0.942809042 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + y = -0.942809042 + -1.666666667
y = -0.942809042 + -1.666666667

Combine like terms: -0.942809042 + -1.666666667 = -2.609475709
y = -2.609475709

Simplifying
y = -2.609475709


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.723857625, -2.609475709}

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