2(k^2-6k-30)=0

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Solution for 2(k^2-6k-30)=0 equation: 


Simplifying
2(k2 + -6k + -30) = 0

Reorder the terms:
2(-30 + -6k + k2) = 0
(-30 * 2 + -6k * 2 + k2 * 2) = 0
(-60 + -12k + 2k2) = 0

Solving
-60 + -12k + 2k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -6k + k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + -6k + k2)' equal to zero and attempt to solve:

Simplifying
-30 + -6k + k2 = 0

Solving
-30 + -6k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -6k + 30 + k2 = 0 + 30

Reorder the terms:
-30 + 30 + -6k + k2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -6k + k2 = 0 + 30
-6k + k2 = 0 + 30

Combine like terms: 0 + 30 = 30
-6k + k2 = 30

The k term is -6k.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6k + 9 + k2 = 30 + 9

Reorder the terms:
9 + -6k + k2 = 30 + 9

Combine like terms: 30 + 9 = 39
9 + -6k + k2 = 39

Factor a perfect square on the left side:
(k + -3)(k + -3) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(k + -3) equal to 6.244997998 and -6.244997998.


Subproblem 1
k + -3 = 6.244997998

Simplifying
k + -3 = 6.244997998

Reorder the terms:
-3 + k = 6.244997998

Solving
-3 + k = 6.244997998

Solving for variable 'k'.

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

Add '3' to each side of the equation.
-3 + 3 + k = 6.244997998 + 3

Combine like terms: -3 + 3 = 0
0 + k = 6.244997998 + 3
k = 6.244997998 + 3

Combine like terms: 6.244997998 + 3 = 9.244997998
k = 9.244997998

Simplifying
k = 9.244997998


Subproblem 2
k + -3 = -6.244997998

Simplifying
k + -3 = -6.244997998

Reorder the terms:
-3 + k = -6.244997998

Solving
-3 + k = -6.244997998

Solving for variable 'k'.

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

Add '3' to each side of the equation.
-3 + 3 + k = -6.244997998 + 3

Combine like terms: -3 + 3 = 0
0 + k = -6.244997998 + 3
k = -6.244997998 + 3

Combine like terms: -6.244997998 + 3 = -3.244997998
k = -3.244997998

Simplifying
k = -3.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {9.244997998, -3.244997998}
Solution
k = {9.244997998, -3.244997998}

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