(7+k)*k=16

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Solution for (7+k)*k=16 equation: 


Simplifying
(7 + k) * k = 16

Reorder the terms for easier multiplication:
k(7 + k) = 16
(7 * k + k * k) = 16
(7k + k2) = 16

Solving
7k + k2 = 16

Solving for variable 'k'.

Reorder the terms:
-16 + 7k + k2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 7k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 7k + 16 + k2 = 0 + 16

Reorder the terms:
-16 + 16 + 7k + k2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 7k + k2 = 0 + 16
7k + k2 = 0 + 16

Combine like terms: 0 + 16 = 16
7k + k2 = 16

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 = 16 + 12.25

Reorder the terms:
12.25 + 7k + k2 = 16 + 12.25

Combine like terms: 16 + 12.25 = 28.25
12.25 + 7k + k2 = 28.25

Factor a perfect square on the left side:
(k + 3.5)(k + 3.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(k + 3.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
k + 3.5 = 5.315072906

Simplifying
k + 3.5 = 5.315072906

Reorder the terms:
3.5 + k = 5.315072906

Solving
3.5 + k = 5.315072906

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 = 5.315072906 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + k = 5.315072906 + -3.5
k = 5.315072906 + -3.5

Combine like terms: 5.315072906 + -3.5 = 1.815072906
k = 1.815072906

Simplifying
k = 1.815072906


Subproblem 2
k + 3.5 = -5.315072906

Simplifying
k + 3.5 = -5.315072906

Reorder the terms:
3.5 + k = -5.315072906

Solving
3.5 + k = -5.315072906

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 = -5.315072906 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + k = -5.315072906 + -3.5
k = -5.315072906 + -3.5

Combine like terms: -5.315072906 + -3.5 = -8.815072906
k = -8.815072906

Simplifying
k = -8.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.815072906, -8.815072906}

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