4k(k+13)+18=0

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Solution for 4k(k+13)+18=0 equation: 


Simplifying
4k(k + 13) + 18 = 0

Reorder the terms:
4k(13 + k) + 18 = 0
(13 * 4k + k * 4k) + 18 = 0
(52k + 4k2) + 18 = 0

Reorder the terms:
18 + 52k + 4k2 = 0

Solving
18 + 52k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 26k + 2k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + 26k + 2k2)' equal to zero and attempt to solve:

Simplifying
9 + 26k + 2k2 = 0

Solving
9 + 26k + 2k2 = 0

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

Divide each side by '2'.
4.5 + 13k + k2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 13k + -4.5 + k2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 13k + k2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 13k + k2 = 0 + -4.5
13k + k2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
13k + k2 = -4.5

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 = -4.5 + 42.25

Reorder the terms:
42.25 + 13k + k2 = -4.5 + 42.25

Combine like terms: -4.5 + 42.25 = 37.75
42.25 + 13k + k2 = 37.75

Factor a perfect square on the left side:
(k + 6.5)(k + 6.5) = 37.75

Calculate the square root of the right side: 6.144102864

Break this problem into two subproblems by setting 
(k + 6.5) equal to 6.144102864 and -6.144102864.


Subproblem 1
k + 6.5 = 6.144102864

Simplifying
k + 6.5 = 6.144102864

Reorder the terms:
6.5 + k = 6.144102864

Solving
6.5 + k = 6.144102864

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 = 6.144102864 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + k = 6.144102864 + -6.5
k = 6.144102864 + -6.5

Combine like terms: 6.144102864 + -6.5 = -0.355897136
k = -0.355897136

Simplifying
k = -0.355897136


Subproblem 2
k + 6.5 = -6.144102864

Simplifying
k + 6.5 = -6.144102864

Reorder the terms:
6.5 + k = -6.144102864

Solving
6.5 + k = -6.144102864

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 = -6.144102864 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + k = -6.144102864 + -6.5
k = -6.144102864 + -6.5

Combine like terms: -6.144102864 + -6.5 = -12.644102864
k = -12.644102864

Simplifying
k = -12.644102864


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.355897136, -12.644102864}
Solution
k = {-0.355897136, -12.644102864}

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