-3k^2+42k-93=0

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Solution for -3k^2+42k-93=0 equation: 


Simplifying
-3k2 + 42k + -93 = 0

Reorder the terms:
-93 + 42k + -3k2 = 0

Solving
-93 + 42k + -3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-31 + 14k + -1k2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-31 + 14k + -1k2)' equal to zero and attempt to solve:

Simplifying
-31 + 14k + -1k2 = 0

Solving
-31 + 14k + -1k2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
31 + -14k + k2 = 0

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -14k + -31 + k2 = 0 + -31

Reorder the terms:
31 + -31 + -14k + k2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -14k + k2 = 0 + -31
-14k + k2 = 0 + -31

Combine like terms: 0 + -31 = -31
-14k + k2 = -31

The k term is -14k.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14k + 49 + k2 = -31 + 49

Reorder the terms:
49 + -14k + k2 = -31 + 49

Combine like terms: -31 + 49 = 18
49 + -14k + k2 = 18

Factor a perfect square on the left side:
(k + -7)(k + -7) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(k + -7) equal to 4.242640687 and -4.242640687.


Subproblem 1
k + -7 = 4.242640687

Simplifying
k + -7 = 4.242640687

Reorder the terms:
-7 + k = 4.242640687

Solving
-7 + k = 4.242640687

Solving for variable 'k'.

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

Add '7' to each side of the equation.
-7 + 7 + k = 4.242640687 + 7

Combine like terms: -7 + 7 = 0
0 + k = 4.242640687 + 7
k = 4.242640687 + 7

Combine like terms: 4.242640687 + 7 = 11.242640687
k = 11.242640687

Simplifying
k = 11.242640687


Subproblem 2
k + -7 = -4.242640687

Simplifying
k + -7 = -4.242640687

Reorder the terms:
-7 + k = -4.242640687

Solving
-7 + k = -4.242640687

Solving for variable 'k'.

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

Add '7' to each side of the equation.
-7 + 7 + k = -4.242640687 + 7

Combine like terms: -7 + 7 = 0
0 + k = -4.242640687 + 7
k = -4.242640687 + 7

Combine like terms: -4.242640687 + 7 = 2.757359313
k = 2.757359313

Simplifying
k = 2.757359313


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {11.242640687, 2.757359313}
Solution
k = {11.242640687, 2.757359313}

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