-k^2-65k+720=0

Solution for -k^2-65k+720=0 equation:

Simplifying
-1k2 + -65k + 720 = 0

Reorder the terms:
720 + -65k + -1k2 = 0

Solving
720 + -65k + -1k2 = 0

Solving for variable 'k'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-720 + 65k + k2 = 0

Move the constant term to the right:

Add '720' to each side of the equation.
-720 + 65k + 720 + k2 = 0 + 720

Reorder the terms:
-720 + 720 + 65k + k2 = 0 + 720

Combine like terms: -720 + 720 = 0
0 + 65k + k2 = 0 + 720
65k + k2 = 0 + 720

Combine like terms: 0 + 720 = 720
65k + k2 = 720

The k term is 65k.  Take half its coefficient (32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
65k + 1056.25 + k2 = 720 + 1056.25

Reorder the terms:
1056.25 + 65k + k2 = 720 + 1056.25

Combine like terms: 720 + 1056.25 = 1776.25
1056.25 + 65k + k2 = 1776.25

Factor a perfect square on the left side:
(k + 32.5)(k + 32.5) = 1776.25

Calculate the square root of the right side: 42.145581026

Break this problem into two subproblems by setting 
(k + 32.5) equal to 42.145581026 and -42.145581026.

Subproblem 1
k + 32.5 = 42.145581026

Simplifying
k + 32.5 = 42.145581026

Reorder the terms:
32.5 + k = 42.145581026

Solving
32.5 + k = 42.145581026

Solving for variable 'k'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + k = 42.145581026 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + k = 42.145581026 + -32.5
k = 42.145581026 + -32.5

Combine like terms: 42.145581026 + -32.5 = 9.645581026
k = 9.645581026

Simplifying
k = 9.645581026

Subproblem 2
k + 32.5 = -42.145581026

Simplifying
k + 32.5 = -42.145581026

Reorder the terms:
32.5 + k = -42.145581026

Solving
32.5 + k = -42.145581026

Solving for variable 'k'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + k = -42.145581026 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + k = -42.145581026 + -32.5
k = -42.145581026 + -32.5

Combine like terms: -42.145581026 + -32.5 = -74.645581026
k = -74.645581026

Simplifying
k = -74.645581026

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {9.645581026, -74.645581026}