9x^2-54x-81=0

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Solution for 9x^2-54x-81=0 equation: 


Simplifying
9x2 + -54x + -81 = 0

Reorder the terms:
-81 + -54x + 9x2 = 0

Solving
-81 + -54x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-9 + -6x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-9 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + -6x + x2 = 0

Solving
-9 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -6x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -6x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -6x + x2 = 0 + 9
-6x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-6x + x2 = 9

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 = 9 + 9

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

Combine like terms: 9 + 9 = 18
9 + -6x + x2 = 18

Factor a perfect square on the left side:
(x + -3)(x + -3) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -3) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + -3 = 4.242640687

Simplifying
x + -3 = 4.242640687

Reorder the terms:
-3 + x = 4.242640687

Solving
-3 + x = 4.242640687

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 = 4.242640687 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.242640687 + 3
x = 4.242640687 + 3

Combine like terms: 4.242640687 + 3 = 7.242640687
x = 7.242640687

Simplifying
x = 7.242640687


Subproblem 2
x + -3 = -4.242640687

Simplifying
x + -3 = -4.242640687

Reorder the terms:
-3 + x = -4.242640687

Solving
-3 + x = -4.242640687

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 = -4.242640687 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.242640687 + 3
x = -4.242640687 + 3

Combine like terms: -4.242640687 + 3 = -1.242640687
x = -1.242640687

Simplifying
x = -1.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.242640687, -1.242640687}
Solution
x = {7.242640687, -1.242640687}

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