12k^2-5k-4=0

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Solution for 12k^2-5k-4=0 equation: 


Simplifying
12k2 + -5k + -4 = 0

Reorder the terms:
-4 + -5k + 12k2 = 0

Solving
-4 + -5k + 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'.
-0.3333333333 + -0.4166666667k + k2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.4166666667k + 0.3333333333 + k2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.4166666667k + k2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.4166666667k + k2 = 0 + 0.3333333333
-0.4166666667k + k2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.4166666667k + k2 = 0.3333333333

The k term is -0.4166666667k.  Take half its coefficient (-0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
-0.4166666667k + 0.04340277781 + k2 = 0.3333333333 + 0.04340277781

Reorder the terms:
0.04340277781 + -0.4166666667k + k2 = 0.3333333333 + 0.04340277781

Combine like terms: 0.3333333333 + 0.04340277781 = 0.37673611111
0.04340277781 + -0.4166666667k + k2 = 0.37673611111

Factor a perfect square on the left side:
(k + -0.2083333334)(k + -0.2083333334) = 0.37673611111

Calculate the square root of the right side: 0.613788328

Break this problem into two subproblems by setting 
(k + -0.2083333334) equal to 0.613788328 and -0.613788328.


Subproblem 1
k + -0.2083333334 = 0.613788328

Simplifying
k + -0.2083333334 = 0.613788328

Reorder the terms:
-0.2083333334 + k = 0.613788328

Solving
-0.2083333334 + k = 0.613788328

Solving for variable 'k'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + k = 0.613788328 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + k = 0.613788328 + 0.2083333334
k = 0.613788328 + 0.2083333334

Combine like terms: 0.613788328 + 0.2083333334 = 0.8221216614
k = 0.8221216614

Simplifying
k = 0.8221216614


Subproblem 2
k + -0.2083333334 = -0.613788328

Simplifying
k + -0.2083333334 = -0.613788328

Reorder the terms:
-0.2083333334 + k = -0.613788328

Solving
-0.2083333334 + k = -0.613788328

Solving for variable 'k'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + k = -0.613788328 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + k = -0.613788328 + 0.2083333334
k = -0.613788328 + 0.2083333334

Combine like terms: -0.613788328 + 0.2083333334 = -0.4054549946
k = -0.4054549946

Simplifying
k = -0.4054549946


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.8221216614, -0.4054549946}

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