u^2-9u-81=0

Solution for u^2-9u-81=0 equation:

Simplifying
u2 + -9u + -81 = 0

Reorder the terms:
-81 + -9u + u2 = 0

Solving
-81 + -9u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -9u + 81 + u2 = 0 + 81

Reorder the terms:
-81 + 81 + -9u + u2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -9u + u2 = 0 + 81
-9u + u2 = 0 + 81

Combine like terms: 0 + 81 = 81
-9u + u2 = 81

The u term is -9u.  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.
-9u + 20.25 + u2 = 81 + 20.25

Reorder the terms:
20.25 + -9u + u2 = 81 + 20.25

Combine like terms: 81 + 20.25 = 101.25
20.25 + -9u + u2 = 101.25

Factor a perfect square on the left side:
(u + -4.5)(u + -4.5) = 101.25

Calculate the square root of the right side: 10.062305899

Break this problem into two subproblems by setting 
(u + -4.5) equal to 10.062305899 and -10.062305899.

Subproblem 1
u + -4.5 = 10.062305899

Simplifying
u + -4.5 = 10.062305899

Reorder the terms:
-4.5 + u = 10.062305899

Solving
-4.5 + u = 10.062305899

Solving for variable 'u'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + u = 10.062305899 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + u = 10.062305899 + 4.5
u = 10.062305899 + 4.5

Combine like terms: 10.062305899 + 4.5 = 14.562305899
u = 14.562305899

Simplifying
u = 14.562305899

Subproblem 2
u + -4.5 = -10.062305899

Simplifying
u + -4.5 = -10.062305899

Reorder the terms:
-4.5 + u = -10.062305899

Solving
-4.5 + u = -10.062305899

Solving for variable 'u'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + u = -10.062305899 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + u = -10.062305899 + 4.5
u = -10.062305899 + 4.5

Combine like terms: -10.062305899 + 4.5 = -5.562305899
u = -5.562305899

Simplifying
u = -5.562305899

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {14.562305899, -5.562305899}