3x^2-27x-3=0

Solution for 3x^2-27x-3=0 equation:

Simplifying
3x2 + -27x + -3 = 0

Reorder the terms:
-3 + -27x + 3x2 = 0

Solving
-3 + -27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -9x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + -9x + x2 = 0

Solving
-1 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -9x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -9x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9x + x2 = 0 + 1
-9x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-9x + x2 = 1

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 = 1 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + -9x + x2 = 21.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
x + -4.5 = 4.609772229

Simplifying
x + -4.5 = 4.609772229

Reorder the terms:
-4.5 + x = 4.609772229

Solving
-4.5 + x = 4.609772229

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 = 4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.609772229 + 4.5
x = 4.609772229 + 4.5

Combine like terms: 4.609772229 + 4.5 = 9.109772229
x = 9.109772229

Simplifying
x = 9.109772229

Subproblem 2
x + -4.5 = -4.609772229

Simplifying
x + -4.5 = -4.609772229

Reorder the terms:
-4.5 + x = -4.609772229

Solving
-4.5 + x = -4.609772229

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 = -4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.609772229 + 4.5
x = -4.609772229 + 4.5

Combine like terms: -4.609772229 + 4.5 = -0.109772229
x = -0.109772229

Simplifying
x = -0.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.109772229, -0.109772229}
Solution
x = {9.109772229, -0.109772229}