k^2-6k-5=0

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Solution for k^2-6k-5=0 equation: 


Simplifying
k2 + -6k + -5 = 0

Reorder the terms:
-5 + -6k + k2 = 0

Solving
-5 + -6k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -6k + 5 + k2 = 0 + 5

Reorder the terms:
-5 + 5 + -6k + k2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6k + k2 = 0 + 5
-6k + k2 = 0 + 5

Combine like terms: 0 + 5 = 5
-6k + k2 = 5

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 = 5 + 9

Reorder the terms:
9 + -6k + k2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + -6k + k2 = 14

Factor a perfect square on the left side:
(k + -3)(k + -3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(k + -3) equal to 3.741657387 and -3.741657387.


Subproblem 1
k + -3 = 3.741657387

Simplifying
k + -3 = 3.741657387

Reorder the terms:
-3 + k = 3.741657387

Solving
-3 + k = 3.741657387

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 = 3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + k = 3.741657387 + 3
k = 3.741657387 + 3

Combine like terms: 3.741657387 + 3 = 6.741657387
k = 6.741657387

Simplifying
k = 6.741657387


Subproblem 2
k + -3 = -3.741657387

Simplifying
k + -3 = -3.741657387

Reorder the terms:
-3 + k = -3.741657387

Solving
-3 + k = -3.741657387

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 = -3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + k = -3.741657387 + 3
k = -3.741657387 + 3

Combine like terms: -3.741657387 + 3 = -0.741657387
k = -0.741657387

Simplifying
k = -0.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {6.741657387, -0.741657387}

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