k^2+3k-72=0

Solution for k^2+3k-72=0 equation:

Simplifying
k2 + 3k + -72 = 0

Reorder the terms:
-72 + 3k + k2 = 0

Solving
-72 + 3k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 3k + 72 + k2 = 0 + 72

Reorder the terms:
-72 + 72 + 3k + k2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 3k + k2 = 0 + 72
3k + k2 = 0 + 72

Combine like terms: 0 + 72 = 72
3k + k2 = 72

The k term is 3k.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3k + 2.25 + k2 = 72 + 2.25

Reorder the terms:
2.25 + 3k + k2 = 72 + 2.25

Combine like terms: 72 + 2.25 = 74.25
2.25 + 3k + k2 = 74.25

Factor a perfect square on the left side:
(k + 1.5)(k + 1.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(k + 1.5) equal to 8.61684397 and -8.61684397.

Subproblem 1
k + 1.5 = 8.61684397

Simplifying
k + 1.5 = 8.61684397

Reorder the terms:
1.5 + k = 8.61684397

Solving
1.5 + k = 8.61684397

Solving for variable 'k'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + k = 8.61684397 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + k = 8.61684397 + -1.5
k = 8.61684397 + -1.5

Combine like terms: 8.61684397 + -1.5 = 7.11684397
k = 7.11684397

Simplifying
k = 7.11684397

Subproblem 2
k + 1.5 = -8.61684397

Simplifying
k + 1.5 = -8.61684397

Reorder the terms:
1.5 + k = -8.61684397

Solving
1.5 + k = -8.61684397

Solving for variable 'k'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + k = -8.61684397 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + k = -8.61684397 + -1.5
k = -8.61684397 + -1.5

Combine like terms: -8.61684397 + -1.5 = -10.11684397
k = -10.11684397

Simplifying
k = -10.11684397

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {7.11684397, -10.11684397}