3k^2+23k-23=0

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Solution for 3k^2+23k-23=0 equation: 


Simplifying
3k2 + 23k + -23 = 0

Reorder the terms:
-23 + 23k + 3k2 = 0

Solving
-23 + 23k + 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'.
-7.666666667 + 7.666666667k + k2 = 0

Move the constant term to the right:

Add '7.666666667' to each side of the equation.
-7.666666667 + 7.666666667k + 7.666666667 + k2 = 0 + 7.666666667

Reorder the terms:
-7.666666667 + 7.666666667 + 7.666666667k + k2 = 0 + 7.666666667

Combine like terms: -7.666666667 + 7.666666667 = 0.000000000
0.000000000 + 7.666666667k + k2 = 0 + 7.666666667
7.666666667k + k2 = 0 + 7.666666667

Combine like terms: 0 + 7.666666667 = 7.666666667
7.666666667k + k2 = 7.666666667

The k term is 7.666666667k.  Take half its coefficient (3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
7.666666667k + 14.69444445 + k2 = 7.666666667 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667k + k2 = 7.666666667 + 14.69444445

Combine like terms: 7.666666667 + 14.69444445 = 22.361111117
14.69444445 + 7.666666667k + k2 = 22.361111117

Factor a perfect square on the left side:
(k + 3.833333334)(k + 3.833333334) = 22.361111117

Calculate the square root of the right side: 4.728753654

Break this problem into two subproblems by setting 
(k + 3.833333334) equal to 4.728753654 and -4.728753654.


Subproblem 1
k + 3.833333334 = 4.728753654

Simplifying
k + 3.833333334 = 4.728753654

Reorder the terms:
3.833333334 + k = 4.728753654

Solving
3.833333334 + k = 4.728753654

Solving for variable 'k'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + k = 4.728753654 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + k = 4.728753654 + -3.833333334
k = 4.728753654 + -3.833333334

Combine like terms: 4.728753654 + -3.833333334 = 0.89542032
k = 0.89542032

Simplifying
k = 0.89542032


Subproblem 2
k + 3.833333334 = -4.728753654

Simplifying
k + 3.833333334 = -4.728753654

Reorder the terms:
3.833333334 + k = -4.728753654

Solving
3.833333334 + k = -4.728753654

Solving for variable 'k'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + k = -4.728753654 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + k = -4.728753654 + -3.833333334
k = -4.728753654 + -3.833333334

Combine like terms: -4.728753654 + -3.833333334 = -8.562086988
k = -8.562086988

Simplifying
k = -8.562086988


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.89542032, -8.562086988}

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