x^2-17x-108=0

Solution for x^2-17x-108=0 equation:

Simplifying
x2 + -17x + -108 = 0

Reorder the terms:
-108 + -17x + x2 = 0

Solving
-108 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '108' to each side of the equation.
-108 + -17x + 108 + x2 = 0 + 108

Reorder the terms:
-108 + 108 + -17x + x2 = 0 + 108

Combine like terms: -108 + 108 = 0
0 + -17x + x2 = 0 + 108
-17x + x2 = 0 + 108

Combine like terms: 0 + 108 = 108
-17x + x2 = 108

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = 108 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 108 + 72.25

Combine like terms: 108 + 72.25 = 180.25
72.25 + -17x + x2 = 180.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 180.25

Calculate the square root of the right side: 13.425721582

Break this problem into two subproblems by setting 
(x + -8.5) equal to 13.425721582 and -13.425721582.

Subproblem 1
x + -8.5 = 13.425721582

Simplifying
x + -8.5 = 13.425721582

Reorder the terms:
-8.5 + x = 13.425721582

Solving
-8.5 + x = 13.425721582

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 13.425721582 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 13.425721582 + 8.5
x = 13.425721582 + 8.5

Combine like terms: 13.425721582 + 8.5 = 21.925721582
x = 21.925721582

Simplifying
x = 21.925721582

Subproblem 2
x + -8.5 = -13.425721582

Simplifying
x + -8.5 = -13.425721582

Reorder the terms:
-8.5 + x = -13.425721582

Solving
-8.5 + x = -13.425721582

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -13.425721582 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -13.425721582 + 8.5
x = -13.425721582 + 8.5

Combine like terms: -13.425721582 + 8.5 = -4.925721582
x = -4.925721582

Simplifying
x = -4.925721582

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.925721582, -4.925721582}