12x^2+2x-5=0

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Solution for 12x^2+2x-5=0 equation: 


Simplifying
12x2 + 2x + -5 = 0

Reorder the terms:
-5 + 2x + 12x2 = 0

Solving
-5 + 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'.
-0.4166666667 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.1666666667x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + 0.1666666667x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + 0.1666666667x + x2 = 0 + 0.4166666667
0.1666666667x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
0.1666666667x + x2 = 0.4166666667

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 = 0.4166666667 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 0.4166666667 + 0.006944444447

Combine like terms: 0.4166666667 + 0.006944444447 = 0.423611111147
0.006944444447 + 0.1666666667x + x2 = 0.423611111147

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 0.423611111147

Calculate the square root of the right side: 0.65085414

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 0.65085414 and -0.65085414.


Subproblem 1
x + 0.08333333335 = 0.65085414

Simplifying
x + 0.08333333335 = 0.65085414

Reorder the terms:
0.08333333335 + x = 0.65085414

Solving
0.08333333335 + x = 0.65085414

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 = 0.65085414 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 0.65085414 + -0.08333333335
x = 0.65085414 + -0.08333333335

Combine like terms: 0.65085414 + -0.08333333335 = 0.56752080665
x = 0.56752080665

Simplifying
x = 0.56752080665


Subproblem 2
x + 0.08333333335 = -0.65085414

Simplifying
x + 0.08333333335 = -0.65085414

Reorder the terms:
0.08333333335 + x = -0.65085414

Solving
0.08333333335 + x = -0.65085414

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 = -0.65085414 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -0.65085414 + -0.08333333335
x = -0.65085414 + -0.08333333335

Combine like terms: -0.65085414 + -0.08333333335 = -0.73418747335
x = -0.73418747335

Simplifying
x = -0.73418747335


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.56752080665, -0.73418747335}

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