3x^2-33x-27=0

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Solution for 3x^2-33x-27=0 equation: 


Simplifying
3x2 + -33x + -27 = 0

Reorder the terms:
-27 + -33x + 3x2 = 0

Solving
-27 + -33x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -11x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + -11x + x2 = 0

Solving
-9 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -11x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -11x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -11x + x2 = 0 + 9
-11x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-11x + x2 = 9

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 9 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 9 + 30.25

Combine like terms: 9 + 30.25 = 39.25
30.25 + -11x + x2 = 39.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.264982043 and -6.264982043.


Subproblem 1
x + -5.5 = 6.264982043

Simplifying
x + -5.5 = 6.264982043

Reorder the terms:
-5.5 + x = 6.264982043

Solving
-5.5 + x = 6.264982043

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 6.264982043 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 6.264982043 + 5.5
x = 6.264982043 + 5.5

Combine like terms: 6.264982043 + 5.5 = 11.764982043
x = 11.764982043

Simplifying
x = 11.764982043


Subproblem 2
x + -5.5 = -6.264982043

Simplifying
x + -5.5 = -6.264982043

Reorder the terms:
-5.5 + x = -6.264982043

Solving
-5.5 + x = -6.264982043

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -6.264982043 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -6.264982043 + 5.5
x = -6.264982043 + 5.5

Combine like terms: -6.264982043 + 5.5 = -0.764982043
x = -0.764982043

Simplifying
x = -0.764982043


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.764982043, -0.764982043}
Solution
x = {11.764982043, -0.764982043}

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