12k^2-k-5=0

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Solution for 12k^2-k-5=0 equation: 


Simplifying
12k2 + -1k + -5 = 0

Reorder the terms:
-5 + -1k + 12k2 = 0

Solving
-5 + -1k + 12k2 = 0

Solving for variable 'k'.

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

Divide each side by '12'.
-0.4166666667 + -0.08333333333k + k2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -0.08333333333k + 0.4166666667 + k2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -0.08333333333k + k2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -0.08333333333k + k2 = 0 + 0.4166666667
-0.08333333333k + k2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
-0.08333333333k + k2 = 0.4166666667

The k term is -0.08333333333k.  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.
-0.08333333333k + 0.001736111111 + k2 = 0.4166666667 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333k + k2 = 0.4166666667 + 0.001736111111

Combine like terms: 0.4166666667 + 0.001736111111 = 0.418402777811
0.001736111111 + -0.08333333333k + k2 = 0.418402777811

Factor a perfect square on the left side:
(k + -0.04166666667)(k + -0.04166666667) = 0.418402777811

Calculate the square root of the right side: 0.646840612

Break this problem into two subproblems by setting 
(k + -0.04166666667) equal to 0.646840612 and -0.646840612.


Subproblem 1
k + -0.04166666667 = 0.646840612

Simplifying
k + -0.04166666667 = 0.646840612

Reorder the terms:
-0.04166666667 + k = 0.646840612

Solving
-0.04166666667 + k = 0.646840612

Solving for variable 'k'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + k = 0.646840612 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + k = 0.646840612 + 0.04166666667
k = 0.646840612 + 0.04166666667

Combine like terms: 0.646840612 + 0.04166666667 = 0.68850727867
k = 0.68850727867

Simplifying
k = 0.68850727867


Subproblem 2
k + -0.04166666667 = -0.646840612

Simplifying
k + -0.04166666667 = -0.646840612

Reorder the terms:
-0.04166666667 + k = -0.646840612

Solving
-0.04166666667 + k = -0.646840612

Solving for variable 'k'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + k = -0.646840612 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + k = -0.646840612 + 0.04166666667
k = -0.646840612 + 0.04166666667

Combine like terms: -0.646840612 + 0.04166666667 = -0.60517394533
k = -0.60517394533

Simplifying
k = -0.60517394533


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.68850727867, -0.60517394533}

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