y^2+3y-81=0

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Solution for y^2+3y-81=0 equation: 


Simplifying
y2 + 3y + -81 = 0

Reorder the terms:
-81 + 3y + y2 = 0

Solving
-81 + 3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 3y + 81 + y2 = 0 + 81

Reorder the terms:
-81 + 81 + 3y + y2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 3y + y2 = 0 + 81
3y + y2 = 0 + 81

Combine like terms: 0 + 81 = 81
3y + y2 = 81

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 81 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 81 + 2.25

Combine like terms: 81 + 2.25 = 83.25
2.25 + 3y + y2 = 83.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 83.25

Calculate the square root of the right side: 9.124143795

Break this problem into two subproblems by setting 
(y + 1.5) equal to 9.124143795 and -9.124143795.


Subproblem 1
y + 1.5 = 9.124143795

Simplifying
y + 1.5 = 9.124143795

Reorder the terms:
1.5 + y = 9.124143795

Solving
1.5 + y = 9.124143795

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 9.124143795 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 9.124143795 + -1.5
y = 9.124143795 + -1.5

Combine like terms: 9.124143795 + -1.5 = 7.624143795
y = 7.624143795

Simplifying
y = 7.624143795


Subproblem 2
y + 1.5 = -9.124143795

Simplifying
y + 1.5 = -9.124143795

Reorder the terms:
1.5 + y = -9.124143795

Solving
1.5 + y = -9.124143795

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -9.124143795 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -9.124143795 + -1.5
y = -9.124143795 + -1.5

Combine like terms: -9.124143795 + -1.5 = -10.624143795
y = -10.624143795

Simplifying
y = -10.624143795


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.624143795, -10.624143795}

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