2(k^2-2k-1)=24

Solution for 2(k^2-2k-1)=24 equation:

Simplifying
2(k2 + -2k + -1) = 24

Reorder the terms:
2(-1 + -2k + k2) = 24
(-1 * 2 + -2k * 2 + k2 * 2) = 24
(-2 + -4k + 2k2) = 24

Solving
-2 + -4k + 2k2 = 24

Solving for variable 'k'.

Reorder the terms:
-2 + -24 + -4k + 2k2 = 24 + -24

Combine like terms: -2 + -24 = -26
-26 + -4k + 2k2 = 24 + -24

Combine like terms: 24 + -24 = 0
-26 + -4k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -2k + k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + -2k + k2)' equal to zero and attempt to solve:

Simplifying
-13 + -2k + k2 = 0

Solving
-13 + -2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -2k + 13 + k2 = 0 + 13

Reorder the terms:
-13 + 13 + -2k + k2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2k + k2 = 0 + 13
-2k + k2 = 0 + 13

Combine like terms: 0 + 13 = 13
-2k + k2 = 13

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = 13 + 1

Reorder the terms:
1 + -2k + k2 = 13 + 1

Combine like terms: 13 + 1 = 14
1 + -2k + k2 = 14

Factor a perfect square on the left side:
(k + -1)(k + -1) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(k + -1) equal to 3.741657387 and -3.741657387.

Subproblem 1
k + -1 = 3.741657387

Simplifying
k + -1 = 3.741657387

Reorder the terms:
-1 + k = 3.741657387

Solving
-1 + k = 3.741657387

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 3.741657387 + 1

Combine like terms: -1 + 1 = 0
0 + k = 3.741657387 + 1
k = 3.741657387 + 1

Combine like terms: 3.741657387 + 1 = 4.741657387
k = 4.741657387

Simplifying
k = 4.741657387

Subproblem 2
k + -1 = -3.741657387

Simplifying
k + -1 = -3.741657387

Reorder the terms:
-1 + k = -3.741657387

Solving
-1 + k = -3.741657387

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -3.741657387 + 1

Combine like terms: -1 + 1 = 0
0 + k = -3.741657387 + 1
k = -3.741657387 + 1

Combine like terms: -3.741657387 + 1 = -2.741657387
k = -2.741657387

Simplifying
k = -2.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.741657387, -2.741657387}
Solution
k = {4.741657387, -2.741657387}