k+4*k+4=k(k+12)

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Solution for k+4*k+4=k(k+12) equation: 


Simplifying
k + 4k + 4 = k(k + 12)

Reorder the terms:
4 + k + 4k = k(k + 12)

Combine like terms: k + 4k = 5k
4 + 5k = k(k + 12)

Reorder the terms:
4 + 5k = k(12 + k)
4 + 5k = (12 * k + k * k)
4 + 5k = (12k + k2)

Solving
4 + 5k = 12k + k2

Solving for variable 'k'.

Combine like terms: 5k + -12k = -7k
4 + -7k + -1k2 = 12k + k2 + -12k + -1k2

Reorder the terms:
4 + -7k + -1k2 = 12k + -12k + k2 + -1k2

Combine like terms: 12k + -12k = 0
4 + -7k + -1k2 = 0 + k2 + -1k2
4 + -7k + -1k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
4 + -7k + -1k2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 7k + k2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 7k + 4 + k2 = 0 + 4

Reorder the terms:
-4 + 4 + 7k + k2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 7k + k2 = 0 + 4
7k + k2 = 0 + 4

Combine like terms: 0 + 4 = 4
7k + k2 = 4

The k term is 7k.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7k + 12.25 + k2 = 4 + 12.25

Reorder the terms:
12.25 + 7k + k2 = 4 + 12.25

Combine like terms: 4 + 12.25 = 16.25
12.25 + 7k + k2 = 16.25

Factor a perfect square on the left side:
(k + 3.5)(k + 3.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(k + 3.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
k + 3.5 = 4.031128874

Simplifying
k + 3.5 = 4.031128874

Reorder the terms:
3.5 + k = 4.031128874

Solving
3.5 + k = 4.031128874

Solving for variable 'k'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + k = 4.031128874 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + k = 4.031128874 + -3.5
k = 4.031128874 + -3.5

Combine like terms: 4.031128874 + -3.5 = 0.531128874
k = 0.531128874

Simplifying
k = 0.531128874


Subproblem 2
k + 3.5 = -4.031128874

Simplifying
k + 3.5 = -4.031128874

Reorder the terms:
3.5 + k = -4.031128874

Solving
3.5 + k = -4.031128874

Solving for variable 'k'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + k = -4.031128874 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + k = -4.031128874 + -3.5
k = -4.031128874 + -3.5

Combine like terms: -4.031128874 + -3.5 = -7.531128874
k = -7.531128874

Simplifying
k = -7.531128874


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.531128874, -7.531128874}

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