12x^2-2x-1=0

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


Simplifying
12x2 + -2x + -1 = 0

Reorder the terms:
-1 + -2x + 12x2 = 0

Solving
-1 + -2x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-0.08333333333 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + -0.1666666667x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + -0.1666666667x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + -0.1666666667x + x2 = 0 + 0.08333333333
-0.1666666667x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
-0.1666666667x + x2 = 0.08333333333

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 0.08333333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 0.08333333333 + 0.006944444447

Combine like terms: 0.08333333333 + 0.006944444447 = 0.090277777777
0.006944444447 + -0.1666666667x + x2 = 0.090277777777

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 0.090277777777

Calculate the square root of the right side: 0.300462606

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 0.300462606 and -0.300462606.


Subproblem 1
x + -0.08333333335 = 0.300462606

Simplifying
x + -0.08333333335 = 0.300462606

Reorder the terms:
-0.08333333335 + x = 0.300462606

Solving
-0.08333333335 + x = 0.300462606

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 0.300462606 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 0.300462606 + 0.08333333335
x = 0.300462606 + 0.08333333335

Combine like terms: 0.300462606 + 0.08333333335 = 0.38379593935
x = 0.38379593935

Simplifying
x = 0.38379593935


Subproblem 2
x + -0.08333333335 = -0.300462606

Simplifying
x + -0.08333333335 = -0.300462606

Reorder the terms:
-0.08333333335 + x = -0.300462606

Solving
-0.08333333335 + x = -0.300462606

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -0.300462606 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -0.300462606 + 0.08333333335
x = -0.300462606 + 0.08333333335

Combine like terms: -0.300462606 + 0.08333333335 = -0.21712927265
x = -0.21712927265

Simplifying
x = -0.21712927265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.38379593935, -0.21712927265}

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