18x^2+12x-1=0

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Solution for 18x^2+12x-1=0 equation: 


Simplifying
18x2 + 12x + -1 = 0

Reorder the terms:
-1 + 12x + 18x2 = 0

Solving
-1 + 12x + 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 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.05555555556' to each side of the equation.
-0.05555555556 + 0.6666666667x + 0.05555555556 + x2 = 0 + 0.05555555556

Reorder the terms:
-0.05555555556 + 0.05555555556 + 0.6666666667x + x2 = 0 + 0.05555555556

Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000
0.00000000000 + 0.6666666667x + x2 = 0 + 0.05555555556
0.6666666667x + x2 = 0 + 0.05555555556

Combine like terms: 0 + 0.05555555556 = 0.05555555556
0.6666666667x + x2 = 0.05555555556

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.05555555556 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.05555555556 + 0.1111111112

Combine like terms: 0.05555555556 + 0.1111111112 = 0.16666666676
0.1111111112 + 0.6666666667x + x2 = 0.16666666676

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.16666666676

Calculate the square root of the right side: 0.408248291

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.408248291 and -0.408248291.


Subproblem 1
x + 0.3333333334 = 0.408248291

Simplifying
x + 0.3333333334 = 0.408248291

Reorder the terms:
0.3333333334 + x = 0.408248291

Solving
0.3333333334 + x = 0.408248291

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.408248291 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.408248291 + -0.3333333334
x = 0.408248291 + -0.3333333334

Combine like terms: 0.408248291 + -0.3333333334 = 0.0749149576
x = 0.0749149576

Simplifying
x = 0.0749149576


Subproblem 2
x + 0.3333333334 = -0.408248291

Simplifying
x + 0.3333333334 = -0.408248291

Reorder the terms:
0.3333333334 + x = -0.408248291

Solving
0.3333333334 + x = -0.408248291

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.408248291 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.408248291 + -0.3333333334
x = -0.408248291 + -0.3333333334

Combine like terms: -0.408248291 + -0.3333333334 = -0.7415816244
x = -0.7415816244

Simplifying
x = -0.7415816244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0749149576, -0.7415816244}

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