y^2+9y-27=0

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Solution for y^2+9y-27=0 equation: 


Simplifying
y2 + 9y + -27 = 0

Reorder the terms:
-27 + 9y + y2 = 0

Solving
-27 + 9y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 9y + 27 + y2 = 0 + 27

Reorder the terms:
-27 + 27 + 9y + y2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 9y + y2 = 0 + 27
9y + y2 = 0 + 27

Combine like terms: 0 + 27 = 27
9y + y2 = 27

The y term is 9y.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9y + 20.25 + y2 = 27 + 20.25

Reorder the terms:
20.25 + 9y + y2 = 27 + 20.25

Combine like terms: 27 + 20.25 = 47.25
20.25 + 9y + y2 = 47.25

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(y + 4.5) equal to 6.873863542 and -6.873863542.


Subproblem 1
y + 4.5 = 6.873863542

Simplifying
y + 4.5 = 6.873863542

Reorder the terms:
4.5 + y = 6.873863542

Solving
4.5 + y = 6.873863542

Solving for variable 'y'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = 6.873863542 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = 6.873863542 + -4.5
y = 6.873863542 + -4.5

Combine like terms: 6.873863542 + -4.5 = 2.373863542
y = 2.373863542

Simplifying
y = 2.373863542


Subproblem 2
y + 4.5 = -6.873863542

Simplifying
y + 4.5 = -6.873863542

Reorder the terms:
4.5 + y = -6.873863542

Solving
4.5 + y = -6.873863542

Solving for variable 'y'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = -6.873863542 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = -6.873863542 + -4.5
y = -6.873863542 + -4.5

Combine like terms: -6.873863542 + -4.5 = -11.373863542
y = -11.373863542

Simplifying
y = -11.373863542


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.373863542, -11.373863542}

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