k(4k+32)=72

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Solution for k(4k+32)=72 equation:


Simplifying
k(4k + 32) = 72

Reorder the terms:
k(32 + 4k) = 72
(32 * k + 4k * k) = 72
(32k + 4k2) = 72

Solving
32k + 4k2 = 72

Solving for variable 'k'.

Reorder the terms:
-72 + 32k + 4k2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 32k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 8k + k2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-18 + 8k + k2)' equal to zero and attempt to solve:

Simplifying
-18 + 8k + k2 = 0

Solving
-18 + 8k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 8k + 18 + k2 = 0 + 18

Reorder the terms:
-18 + 18 + 8k + k2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 8k + k2 = 0 + 18
8k + k2 = 0 + 18

Combine like terms: 0 + 18 = 18
8k + k2 = 18

The k term is 8k.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8k + 16 + k2 = 18 + 16

Reorder the terms:
16 + 8k + k2 = 18 + 16

Combine like terms: 18 + 16 = 34
16 + 8k + k2 = 34

Factor a perfect square on the left side:
(k + 4)(k + 4) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(k + 4) equal to 5.830951895 and -5.830951895.


Subproblem 1
k + 4 = 5.830951895

Simplifying
k + 4 = 5.830951895

Reorder the terms:
4 + k = 5.830951895

Solving
4 + k = 5.830951895

Solving for variable 'k'.

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

Add '-4' to each side of the equation.
4 + -4 + k = 5.830951895 + -4

Combine like terms: 4 + -4 = 0
0 + k = 5.830951895 + -4
k = 5.830951895 + -4

Combine like terms: 5.830951895 + -4 = 1.830951895
k = 1.830951895

Simplifying
k = 1.830951895


Subproblem 2
k + 4 = -5.830951895

Simplifying
k + 4 = -5.830951895

Reorder the terms:
4 + k = -5.830951895

Solving
4 + k = -5.830951895

Solving for variable 'k'.

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

Add '-4' to each side of the equation.
4 + -4 + k = -5.830951895 + -4

Combine like terms: 4 + -4 = 0
0 + k = -5.830951895 + -4
k = -5.830951895 + -4

Combine like terms: -5.830951895 + -4 = -9.830951895
k = -9.830951895

Simplifying
k = -9.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.830951895, -9.830951895}
Solution
k = {1.830951895, -9.830951895}

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