3k^2-26k+15=0

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Solution for 3k^2-26k+15=0 equation: 


Simplifying
3k2 + -26k + 15 = 0

Reorder the terms:
15 + -26k + 3k2 = 0

Solving
15 + -26k + 3k2 = 0

Solving for variable 'k'.

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

Divide each side by '3'.
5 + -8.666666667k + k2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8.666666667k + -5 + k2 = 0 + -5

Reorder the terms:
5 + -5 + -8.666666667k + k2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8.666666667k + k2 = 0 + -5
-8.666666667k + k2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8.666666667k + k2 = -5

The k term is -8.666666667k.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667k + 18.77777778 + k2 = -5 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667k + k2 = -5 + 18.77777778

Combine like terms: -5 + 18.77777778 = 13.77777778
18.77777778 + -8.666666667k + k2 = 13.77777778

Factor a perfect square on the left side:
(k + -4.333333334)(k + -4.333333334) = 13.77777778

Calculate the square root of the right side: 3.711842909

Break this problem into two subproblems by setting 
(k + -4.333333334) equal to 3.711842909 and -3.711842909.


Subproblem 1
k + -4.333333334 = 3.711842909

Simplifying
k + -4.333333334 = 3.711842909

Reorder the terms:
-4.333333334 + k = 3.711842909

Solving
-4.333333334 + k = 3.711842909

Solving for variable 'k'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + k = 3.711842909 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + k = 3.711842909 + 4.333333334
k = 3.711842909 + 4.333333334

Combine like terms: 3.711842909 + 4.333333334 = 8.045176243
k = 8.045176243

Simplifying
k = 8.045176243


Subproblem 2
k + -4.333333334 = -3.711842909

Simplifying
k + -4.333333334 = -3.711842909

Reorder the terms:
-4.333333334 + k = -3.711842909

Solving
-4.333333334 + k = -3.711842909

Solving for variable 'k'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + k = -3.711842909 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + k = -3.711842909 + 4.333333334
k = -3.711842909 + 4.333333334

Combine like terms: -3.711842909 + 4.333333334 = 0.621490425
k = 0.621490425

Simplifying
k = 0.621490425


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {8.045176243, 0.621490425}

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