6k^2-42k-72=0

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Solution for 6k^2-42k-72=0 equation: 


Simplifying
6k2 + -42k + -72 = 0

Reorder the terms:
-72 + -42k + 6k2 = 0

Solving
-72 + -42k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + -7k + k2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-12 + -7k + k2)' equal to zero and attempt to solve:

Simplifying
-12 + -7k + k2 = 0

Solving
-12 + -7k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -7k + 12 + k2 = 0 + 12

Reorder the terms:
-12 + 12 + -7k + k2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -7k + k2 = 0 + 12
-7k + k2 = 0 + 12

Combine like terms: 0 + 12 = 12
-7k + k2 = 12

The k term is -7k.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7k + 12.25 + k2 = 12 + 12.25

Reorder the terms:
12.25 + -7k + k2 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + -7k + k2 = 24.25

Factor a perfect square on the left side:
(k + -3.5)(k + -3.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(k + -3.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
k + -3.5 = 4.924428901

Simplifying
k + -3.5 = 4.924428901

Reorder the terms:
-3.5 + k = 4.924428901

Solving
-3.5 + k = 4.924428901

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k = 4.924428901 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = 4.924428901 + 3.5
k = 4.924428901 + 3.5

Combine like terms: 4.924428901 + 3.5 = 8.424428901
k = 8.424428901

Simplifying
k = 8.424428901


Subproblem 2
k + -3.5 = -4.924428901

Simplifying
k + -3.5 = -4.924428901

Reorder the terms:
-3.5 + k = -4.924428901

Solving
-3.5 + k = -4.924428901

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k = -4.924428901 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = -4.924428901 + 3.5
k = -4.924428901 + 3.5

Combine like terms: -4.924428901 + 3.5 = -1.424428901
k = -1.424428901

Simplifying
k = -1.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {8.424428901, -1.424428901}
Solution
k = {8.424428901, -1.424428901}

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