x^2-6x-81=0

Solution for x^2-6x-81=0 equation:

Simplifying
x2 + -6x + -81 = 0

Reorder the terms:
-81 + -6x + x2 = 0

Solving
-81 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -6x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -6x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -6x + x2 = 0 + 81
-6x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-6x + x2 = 81

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 81 + 9

Reorder the terms:
9 + -6x + x2 = 81 + 9

Combine like terms: 81 + 9 = 90
9 + -6x + x2 = 90

Factor a perfect square on the left side:
(x + -3)(x + -3) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(x + -3) equal to 9.486832981 and -9.486832981.

Subproblem 1
x + -3 = 9.486832981

Simplifying
x + -3 = 9.486832981

Reorder the terms:
-3 + x = 9.486832981

Solving
-3 + x = 9.486832981

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 9.486832981 + 3

Combine like terms: -3 + 3 = 0
0 + x = 9.486832981 + 3
x = 9.486832981 + 3

Combine like terms: 9.486832981 + 3 = 12.486832981
x = 12.486832981

Simplifying
x = 12.486832981

Subproblem 2
x + -3 = -9.486832981

Simplifying
x + -3 = -9.486832981

Reorder the terms:
-3 + x = -9.486832981

Solving
-3 + x = -9.486832981

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -9.486832981 + 3

Combine like terms: -3 + 3 = 0
0 + x = -9.486832981 + 3
x = -9.486832981 + 3

Combine like terms: -9.486832981 + 3 = -6.486832981
x = -6.486832981

Simplifying
x = -6.486832981

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.486832981, -6.486832981}