0=x^2-29x-108

Solution for 0=x^2-29x-108 equation:

Simplifying
0 = x2 + -29x + -108

Reorder the terms:
0 = -108 + -29x + x2

Solving
0 = -108 + -29x + x2

Solving for variable 'x'.

Combine like terms: 0 + 108 = 108
108 + 29x + -1x2 = -108 + -29x + x2 + 108 + 29x + -1x2

Reorder the terms:
108 + 29x + -1x2 = -108 + 108 + -29x + 29x + x2 + -1x2

Combine like terms: -108 + 108 = 0
108 + 29x + -1x2 = 0 + -29x + 29x + x2 + -1x2
108 + 29x + -1x2 = -29x + 29x + x2 + -1x2

Combine like terms: -29x + 29x = 0
108 + 29x + -1x2 = 0 + x2 + -1x2
108 + 29x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
108 + 29x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-108 + -29x + x2 = 0

Move the constant term to the right:

Add '108' to each side of the equation.
-108 + -29x + 108 + x2 = 0 + 108

Reorder the terms:
-108 + 108 + -29x + x2 = 0 + 108

Combine like terms: -108 + 108 = 0
0 + -29x + x2 = 0 + 108
-29x + x2 = 0 + 108

Combine like terms: 0 + 108 = 108
-29x + x2 = 108

The x term is -29x.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x + 210.25 + x2 = 108 + 210.25

Reorder the terms:
210.25 + -29x + x2 = 108 + 210.25

Combine like terms: 108 + 210.25 = 318.25
210.25 + -29x + x2 = 318.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 318.25

Calculate the square root of the right side: 17.839562775

Break this problem into two subproblems by setting 
(x + -14.5) equal to 17.839562775 and -17.839562775.

Subproblem 1
x + -14.5 = 17.839562775

Simplifying
x + -14.5 = 17.839562775

Reorder the terms:
-14.5 + x = 17.839562775

Solving
-14.5 + x = 17.839562775

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = 17.839562775 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = 17.839562775 + 14.5
x = 17.839562775 + 14.5

Combine like terms: 17.839562775 + 14.5 = 32.339562775
x = 32.339562775

Simplifying
x = 32.339562775

Subproblem 2
x + -14.5 = -17.839562775

Simplifying
x + -14.5 = -17.839562775

Reorder the terms:
-14.5 + x = -17.839562775

Solving
-14.5 + x = -17.839562775

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = -17.839562775 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = -17.839562775 + 14.5
x = -17.839562775 + 14.5

Combine like terms: -17.839562775 + 14.5 = -3.339562775
x = -3.339562775

Simplifying
x = -3.339562775

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.339562775, -3.339562775}