4k(k+13)=13

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Solution for 4k(k+13)=13 equation: 


Simplifying
4k(k + 13) = 13

Reorder the terms:
4k(13 + k) = 13
(13 * 4k + k * 4k) = 13
(52k + 4k2) = 13

Solving
52k + 4k2 = 13

Solving for variable 'k'.

Reorder the terms:
-13 + 52k + 4k2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 52k + 4k2 = 0

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

Divide each side by '4'.
-3.25 + 13k + k2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 13k + 3.25 + k2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 13k + k2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 13k + k2 = 0 + 3.25
13k + k2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
13k + k2 = 3.25

The k term is 13k.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13k + 42.25 + k2 = 3.25 + 42.25

Reorder the terms:
42.25 + 13k + k2 = 3.25 + 42.25

Combine like terms: 3.25 + 42.25 = 45.5
42.25 + 13k + k2 = 45.5

Factor a perfect square on the left side:
(k + 6.5)(k + 6.5) = 45.5

Calculate the square root of the right side: 6.745368782

Break this problem into two subproblems by setting 
(k + 6.5) equal to 6.745368782 and -6.745368782.


Subproblem 1
k + 6.5 = 6.745368782

Simplifying
k + 6.5 = 6.745368782

Reorder the terms:
6.5 + k = 6.745368782

Solving
6.5 + k = 6.745368782

Solving for variable 'k'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + k = 6.745368782 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + k = 6.745368782 + -6.5
k = 6.745368782 + -6.5

Combine like terms: 6.745368782 + -6.5 = 0.245368782
k = 0.245368782

Simplifying
k = 0.245368782


Subproblem 2
k + 6.5 = -6.745368782

Simplifying
k + 6.5 = -6.745368782

Reorder the terms:
6.5 + k = -6.745368782

Solving
6.5 + k = -6.745368782

Solving for variable 'k'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + k = -6.745368782 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + k = -6.745368782 + -6.5
k = -6.745368782 + -6.5

Combine like terms: -6.745368782 + -6.5 = -13.245368782
k = -13.245368782

Simplifying
k = -13.245368782


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.245368782, -13.245368782}

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