s^2-56s-s^3=0

Solution for s^2-56s-s^3=0 equation:

Simplifying
s2 + -56s + -1s3 = 0

Reorder the terms:
-56s + s2 + -1s3 = 0

Solving
-56s + s2 + -1s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), 's'.
s(-56 + s + -1s2) = 0

Subproblem 1
Set the factor 's' equal to zero and attempt to solve:

Simplifying
s = 0

Solving
s = 0

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

Simplifying
s = 0
Subproblem 2
Set the factor '(-56 + s + -1s2)' equal to zero and attempt to solve:

Simplifying
-56 + s + -1s2 = 0

Solving
-56 + s + -1s2 = 0

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

Divide each side by '-1'.
56 + -1s + s2 = 0

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + -1s + -56 + s2 = 0 + -56

Reorder the terms:
56 + -56 + -1s + s2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -1s + s2 = 0 + -56
-1s + s2 = 0 + -56

Combine like terms: 0 + -56 = -56
-1s + s2 = -56

The s term is s.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1s + 0.25 + s2 = -56 + 0.25

Reorder the terms:
0.25 + -1s + s2 = -56 + 0.25

Combine like terms: -56 + 0.25 = -55.75
0.25 + -1s + s2 = -55.75

Factor a perfect square on the left side:
(s + 0.5)(s + 0.5) = -55.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
s = {0}