(6x^2)+.5x-.125=0

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Solution for (6x^2)+.5x-.125=0 equation: 


Simplifying
(6x2) + 0.5x + -0.125 = 0

Reorder the terms:
-0.125 + 0.5x + (6x2) = 0

Solving
-0.125 + 0.5x + (6x2) = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.02083333333 + 0.08333333333x + x2 = 0

Move the constant term to the right:

Add '0.02083333333' to each side of the equation.
-0.02083333333 + 0.08333333333x + 0.02083333333 + x2 = 0 + 0.02083333333

Reorder the terms:
-0.02083333333 + 0.02083333333 + 0.08333333333x + x2 = 0 + 0.02083333333

Combine like terms: -0.02083333333 + 0.02083333333 = 0.00000000000
0.00000000000 + 0.08333333333x + x2 = 0 + 0.02083333333
0.08333333333x + x2 = 0 + 0.02083333333

Combine like terms: 0 + 0.02083333333 = 0.02083333333
0.08333333333x + x2 = 0.02083333333

The x term is 0.08333333333x.  Take half its coefficient (0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
0.08333333333x + 0.001736111111 + x2 = 0.02083333333 + 0.001736111111

Reorder the terms:
0.001736111111 + 0.08333333333x + x2 = 0.02083333333 + 0.001736111111

Combine like terms: 0.02083333333 + 0.001736111111 = 0.022569444441
0.001736111111 + 0.08333333333x + x2 = 0.022569444441

Factor a perfect square on the left side:
((x) + 0.04166666667)((x) + 0.04166666667) = 0.022569444441

Calculate the square root of the right side: 0.150231303

Break this problem into two subproblems by setting 
((x) + 0.04166666667) equal to 0.150231303 and -0.150231303.


Subproblem 1
(x) + 0.04166666667 = 0.150231303

Simplifying
(x) + 0.04166666667 = 0.150231303
x + 0.04166666667 = 0.150231303

Reorder the terms:
0.04166666667 + x = 0.150231303

Solving
0.04166666667 + x = 0.150231303

Solving for variable 'x'.

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

Add '-0.04166666667' to each side of the equation.
0.04166666667 + -0.04166666667 + x = 0.150231303 + -0.04166666667

Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000
0.00000000000 + x = 0.150231303 + -0.04166666667
x = 0.150231303 + -0.04166666667

Combine like terms: 0.150231303 + -0.04166666667 = 0.10856463633
x = 0.10856463633

Simplifying
x = 0.10856463633


Subproblem 2
(x) + 0.04166666667 = -0.150231303

Simplifying
(x) + 0.04166666667 = -0.150231303
x + 0.04166666667 = -0.150231303

Reorder the terms:
0.04166666667 + x = -0.150231303

Solving
0.04166666667 + x = -0.150231303

Solving for variable 'x'.

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

Add '-0.04166666667' to each side of the equation.
0.04166666667 + -0.04166666667 + x = -0.150231303 + -0.04166666667

Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000
0.00000000000 + x = -0.150231303 + -0.04166666667
x = -0.150231303 + -0.04166666667

Combine like terms: -0.150231303 + -0.04166666667 = -0.19189796967
x = -0.19189796967

Simplifying
x = -0.19189796967


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.10856463633, -0.19189796967}

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