k^2+16k+4=0

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Solution for k^2+16k+4=0 equation: 


Simplifying
k2 + 16k + 4 = 0

Reorder the terms:
4 + 16k + k2 = 0

Solving
4 + 16k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 16k + -4 + k2 = 0 + -4

Reorder the terms:
4 + -4 + 16k + k2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 16k + k2 = 0 + -4
16k + k2 = 0 + -4

Combine like terms: 0 + -4 = -4
16k + k2 = -4

The k term is 16k.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16k + 64 + k2 = -4 + 64

Reorder the terms:
64 + 16k + k2 = -4 + 64

Combine like terms: -4 + 64 = 60
64 + 16k + k2 = 60

Factor a perfect square on the left side:
(k + 8)(k + 8) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(k + 8) equal to 7.745966692 and -7.745966692.


Subproblem 1
k + 8 = 7.745966692

Simplifying
k + 8 = 7.745966692

Reorder the terms:
8 + k = 7.745966692

Solving
8 + k = 7.745966692

Solving for variable 'k'.

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

Add '-8' to each side of the equation.
8 + -8 + k = 7.745966692 + -8

Combine like terms: 8 + -8 = 0
0 + k = 7.745966692 + -8
k = 7.745966692 + -8

Combine like terms: 7.745966692 + -8 = -0.254033308
k = -0.254033308

Simplifying
k = -0.254033308


Subproblem 2
k + 8 = -7.745966692

Simplifying
k + 8 = -7.745966692

Reorder the terms:
8 + k = -7.745966692

Solving
8 + k = -7.745966692

Solving for variable 'k'.

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

Add '-8' to each side of the equation.
8 + -8 + k = -7.745966692 + -8

Combine like terms: 8 + -8 = 0
0 + k = -7.745966692 + -8
k = -7.745966692 + -8

Combine like terms: -7.745966692 + -8 = -15.745966692
k = -15.745966692

Simplifying
k = -15.745966692


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.254033308, -15.745966692}

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