4k(k+2)=2

Solution for 4k(k+2)=2 equation:

Simplifying
4k(k + 2) = 2

Reorder the terms:
4k(2 + k) = 2
(2 * 4k + k * 4k) = 2
(8k + 4k2) = 2

Solving
8k + 4k2 = 2

Solving for variable 'k'.

Reorder the terms:
-2 + 8k + 4k2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 8k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4k + 2k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 4k + 2k2)' equal to zero and attempt to solve:

Simplifying
-1 + 4k + 2k2 = 0

Solving
-1 + 4k + 2k2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + 2k + k2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2k + 0.5 + k2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2k + k2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2k + k2 = 0 + 0.5
2k + k2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2k + k2 = 0.5

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 = 0.5 + 1

Reorder the terms:
1 + 2k + k2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + 2k + k2 = 1.5

Factor a perfect square on the left side:
(k + 1)(k + 1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(k + 1) equal to 1.224744871 and -1.224744871.

Subproblem 1
k + 1 = 1.224744871

Simplifying
k + 1 = 1.224744871

Reorder the terms:
1 + k = 1.224744871

Solving
1 + k = 1.224744871

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 = 1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + k = 1.224744871 + -1
k = 1.224744871 + -1

Combine like terms: 1.224744871 + -1 = 0.224744871
k = 0.224744871

Simplifying
k = 0.224744871

Subproblem 2
k + 1 = -1.224744871

Simplifying
k + 1 = -1.224744871

Reorder the terms:
1 + k = -1.224744871

Solving
1 + k = -1.224744871

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 = -1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + k = -1.224744871 + -1
k = -1.224744871 + -1

Combine like terms: -1.224744871 + -1 = -2.224744871
k = -2.224744871

Simplifying
k = -2.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.224744871, -2.224744871}
Solution
k = {0.224744871, -2.224744871}