3x^2-162x-27=0

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Solution for 3x^2-162x-27=0 equation: 


Simplifying
3x2 + -162x + -27 = 0

Reorder the terms:
-27 + -162x + 3x2 = 0

Solving
-27 + -162x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -54x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + -54x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + -54x + x2 = 0

Solving
-9 + -54x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -54x + 9 + x2 = 0 + 9

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

Combine like terms: -9 + 9 = 0
0 + -54x + x2 = 0 + 9
-54x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-54x + x2 = 9

The x term is -54x.  Take half its coefficient (-27).
Square it (729) and add it to both sides.

Add '729' to each side of the equation.
-54x + 729 + x2 = 9 + 729

Reorder the terms:
729 + -54x + x2 = 9 + 729

Combine like terms: 9 + 729 = 738
729 + -54x + x2 = 738

Factor a perfect square on the left side:
(x + -27)(x + -27) = 738

Calculate the square root of the right side: 27.166155414

Break this problem into two subproblems by setting 
(x + -27) equal to 27.166155414 and -27.166155414.


Subproblem 1
x + -27 = 27.166155414

Simplifying
x + -27 = 27.166155414

Reorder the terms:
-27 + x = 27.166155414

Solving
-27 + x = 27.166155414

Solving for variable 'x'.

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

Add '27' to each side of the equation.
-27 + 27 + x = 27.166155414 + 27

Combine like terms: -27 + 27 = 0
0 + x = 27.166155414 + 27
x = 27.166155414 + 27

Combine like terms: 27.166155414 + 27 = 54.166155414
x = 54.166155414

Simplifying
x = 54.166155414


Subproblem 2
x + -27 = -27.166155414

Simplifying
x + -27 = -27.166155414

Reorder the terms:
-27 + x = -27.166155414

Solving
-27 + x = -27.166155414

Solving for variable 'x'.

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

Add '27' to each side of the equation.
-27 + 27 + x = -27.166155414 + 27

Combine like terms: -27 + 27 = 0
0 + x = -27.166155414 + 27
x = -27.166155414 + 27

Combine like terms: -27.166155414 + 27 = -0.166155414
x = -0.166155414

Simplifying
x = -0.166155414


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.166155414, -0.166155414}
Solution
x = {54.166155414, -0.166155414}

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