x^2-9x-108=0

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Solution for x^2-9x-108=0 equation:


Simplifying
x2 + -9x + -108 = 0

Reorder the terms:
-108 + -9x + x2 = 0

Solving
-108 + -9x + 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 + -9x + 108 + x2 = 0 + 108

Reorder the terms:
-108 + 108 + -9x + x2 = 0 + 108

Combine like terms: -108 + 108 = 0
0 + -9x + x2 = 0 + 108
-9x + x2 = 0 + 108

Combine like terms: 0 + 108 = 108
-9x + x2 = 108

The x term is -9x.  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.
-9x + 20.25 + x2 = 108 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 108 + 20.25

Combine like terms: 108 + 20.25 = 128.25
20.25 + -9x + x2 = 128.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 128.25

Calculate the square root of the right side: 11.324751653

Break this problem into two subproblems by setting 
(x + -4.5) equal to 11.324751653 and -11.324751653.

Subproblem 1

x + -4.5 = 11.324751653 Simplifying x + -4.5 = 11.324751653 Reorder the terms: -4.5 + x = 11.324751653 Solving -4.5 + x = 11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 11.324751653 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 11.324751653 + 4.5 x = 11.324751653 + 4.5 Combine like terms: 11.324751653 + 4.5 = 15.824751653 x = 15.824751653 Simplifying x = 15.824751653

Subproblem 2

x + -4.5 = -11.324751653 Simplifying x + -4.5 = -11.324751653 Reorder the terms: -4.5 + x = -11.324751653 Solving -4.5 + x = -11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -11.324751653 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -11.324751653 + 4.5 x = -11.324751653 + 4.5 Combine like terms: -11.324751653 + 4.5 = -6.824751653 x = -6.824751653 Simplifying x = -6.824751653

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.824751653, -6.824751653}

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