k^2-4k-2=0

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Solution for k^2-4k-2=0 equation: 


Simplifying
k2 + -4k + -2 = 0

Reorder the terms:
-2 + -4k + k2 = 0

Solving
-2 + -4k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + -4k + k2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4k + k2 = 0 + 2
-4k + k2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4k + k2 = 2

The k term is -4k.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4k + 4 + k2 = 2 + 4

Reorder the terms:
4 + -4k + k2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + -4k + k2 = 6

Factor a perfect square on the left side:
(k + -2)(k + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(k + -2) equal to 2.449489743 and -2.449489743.


Subproblem 1
k + -2 = 2.449489743

Simplifying
k + -2 = 2.449489743

Reorder the terms:
-2 + k = 2.449489743

Solving
-2 + k = 2.449489743

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + k = 2.449489743 + 2
k = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
k = 4.449489743

Simplifying
k = 4.449489743


Subproblem 2
k + -2 = -2.449489743

Simplifying
k + -2 = -2.449489743

Reorder the terms:
-2 + k = -2.449489743

Solving
-2 + k = -2.449489743

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + k = -2.449489743 + 2
k = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
k = -0.449489743

Simplifying
k = -0.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.449489743, -0.449489743}

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