x^2-10x-108=0

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Solution for x^2-10x-108=0 equation: 


Simplifying
x2 + -10x + -108 = 0

Reorder the terms:
-108 + -10x + x2 = 0

Solving
-108 + -10x + 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 + -10x + 108 + x2 = 0 + 108

Reorder the terms:
-108 + 108 + -10x + x2 = 0 + 108

Combine like terms: -108 + 108 = 0
0 + -10x + x2 = 0 + 108
-10x + x2 = 0 + 108

Combine like terms: 0 + 108 = 108
-10x + x2 = 108

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 108 + 25

Reorder the terms:
25 + -10x + x2 = 108 + 25

Combine like terms: 108 + 25 = 133
25 + -10x + x2 = 133

Factor a perfect square on the left side:
(x + -5)(x + -5) = 133

Calculate the square root of the right side: 11.532562595

Break this problem into two subproblems by setting 
(x + -5) equal to 11.532562595 and -11.532562595.


Subproblem 1
x + -5 = 11.532562595

Simplifying
x + -5 = 11.532562595

Reorder the terms:
-5 + x = 11.532562595

Solving
-5 + x = 11.532562595

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 11.532562595 + 5

Combine like terms: -5 + 5 = 0
0 + x = 11.532562595 + 5
x = 11.532562595 + 5

Combine like terms: 11.532562595 + 5 = 16.532562595
x = 16.532562595

Simplifying
x = 16.532562595


Subproblem 2
x + -5 = -11.532562595

Simplifying
x + -5 = -11.532562595

Reorder the terms:
-5 + x = -11.532562595

Solving
-5 + x = -11.532562595

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -11.532562595 + 5

Combine like terms: -5 + 5 = 0
0 + x = -11.532562595 + 5
x = -11.532562595 + 5

Combine like terms: -11.532562595 + 5 = -6.532562595
x = -6.532562595

Simplifying
x = -6.532562595


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.532562595, -6.532562595}

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