2k^2+8k+4=0

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Solution for 2k^2+8k+4=0 equation: 


Simplifying
2k2 + 8k + 4 = 0

Reorder the terms:
4 + 8k + 2k2 = 0

Solving
4 + 8k + 2k2 = 0

Solving for variable 'k'.

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

Ignore the factor 2.

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

Simplifying
2 + 4k + k2 = 0

Solving
2 + 4k + k2 = 0

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 = 2
4 + 4k + k2 = 2

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

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(k + 2) equal to 1.414213562 and -1.414213562.


Subproblem 1
k + 2 = 1.414213562

Simplifying
k + 2 = 1.414213562

Reorder the terms:
2 + k = 1.414213562

Solving
2 + k = 1.414213562

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 = 1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + k = 1.414213562 + -2
k = 1.414213562 + -2

Combine like terms: 1.414213562 + -2 = -0.585786438
k = -0.585786438

Simplifying
k = -0.585786438


Subproblem 2
k + 2 = -1.414213562

Simplifying
k + 2 = -1.414213562

Reorder the terms:
2 + k = -1.414213562

Solving
2 + k = -1.414213562

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 = -1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + k = -1.414213562 + -2
k = -1.414213562 + -2

Combine like terms: -1.414213562 + -2 = -3.414213562
k = -3.414213562

Simplifying
k = -3.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.585786438, -3.414213562}
Solution
k = {-0.585786438, -3.414213562}

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