18x^2-6x-1=0

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Solution for 18x^2-6x-1=0 equation: 


Simplifying
18x2 + -6x + -1 = 0

Reorder the terms:
-1 + -6x + 18x2 = 0

Solving
-1 + -6x + 18x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
18 the coefficient of the squared term: 

Divide each side by '18'.
-0.05555555556 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.05555555556' to each side of the equation.
-0.05555555556 + -0.3333333333x + 0.05555555556 + x2 = 0 + 0.05555555556

Reorder the terms:
-0.05555555556 + 0.05555555556 + -0.3333333333x + x2 = 0 + 0.05555555556

Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000
0.00000000000 + -0.3333333333x + x2 = 0 + 0.05555555556
-0.3333333333x + x2 = 0 + 0.05555555556

Combine like terms: 0 + 0.05555555556 = 0.05555555556
-0.3333333333x + x2 = 0.05555555556

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 0.05555555556 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 0.05555555556 + 0.02777777779

Combine like terms: 0.05555555556 + 0.02777777779 = 0.08333333335
0.02777777779 + -0.3333333333x + x2 = 0.08333333335

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 0.08333333335

Calculate the square root of the right side: 0.288675135

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 0.288675135 and -0.288675135.


Subproblem 1
x + -0.1666666667 = 0.288675135

Simplifying
x + -0.1666666667 = 0.288675135

Reorder the terms:
-0.1666666667 + x = 0.288675135

Solving
-0.1666666667 + x = 0.288675135

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 0.288675135 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 0.288675135 + 0.1666666667
x = 0.288675135 + 0.1666666667

Combine like terms: 0.288675135 + 0.1666666667 = 0.4553418017
x = 0.4553418017

Simplifying
x = 0.4553418017


Subproblem 2
x + -0.1666666667 = -0.288675135

Simplifying
x + -0.1666666667 = -0.288675135

Reorder the terms:
-0.1666666667 + x = -0.288675135

Solving
-0.1666666667 + x = -0.288675135

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -0.288675135 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -0.288675135 + 0.1666666667
x = -0.288675135 + 0.1666666667

Combine like terms: -0.288675135 + 0.1666666667 = -0.1220084683
x = -0.1220084683

Simplifying
x = -0.1220084683


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4553418017, -0.1220084683}

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