3x^2-18x-162=0

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Solution for 3x^2-18x-162=0 equation: 


Simplifying
3x2 + -18x + -162 = 0

Reorder the terms:
-162 + -18x + 3x2 = 0

Solving
-162 + -18x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-54 + -6x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-54 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-54 + -6x + x2 = 0

Solving
-54 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -6x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -6x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -6x + x2 = 0 + 54
-6x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-6x + x2 = 54

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 = 54 + 9

Reorder the terms:
9 + -6x + x2 = 54 + 9

Combine like terms: 54 + 9 = 63
9 + -6x + x2 = 63

Factor a perfect square on the left side:
(x + -3)(x + -3) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + -3) equal to 7.937253933 and -7.937253933.


Subproblem 1
x + -3 = 7.937253933

Simplifying
x + -3 = 7.937253933

Reorder the terms:
-3 + x = 7.937253933

Solving
-3 + x = 7.937253933

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 = 7.937253933 + 3

Combine like terms: -3 + 3 = 0
0 + x = 7.937253933 + 3
x = 7.937253933 + 3

Combine like terms: 7.937253933 + 3 = 10.937253933
x = 10.937253933

Simplifying
x = 10.937253933


Subproblem 2
x + -3 = -7.937253933

Simplifying
x + -3 = -7.937253933

Reorder the terms:
-3 + x = -7.937253933

Solving
-3 + x = -7.937253933

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 = -7.937253933 + 3

Combine like terms: -3 + 3 = 0
0 + x = -7.937253933 + 3
x = -7.937253933 + 3

Combine like terms: -7.937253933 + 3 = -4.937253933
x = -4.937253933

Simplifying
x = -4.937253933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.937253933, -4.937253933}
Solution
x = {10.937253933, -4.937253933}

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