5s^2-6s-16=0

Solution for 5s^2-6s-16=0 equation:

Simplifying
5s2 + -6s + -16 = 0

Reorder the terms:
-16 + -6s + 5s2 = 0

Solving
-16 + -6s + 5s2 = 0

Solving for variable 's'.

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

Divide each side by '5'.
-3.2 + -1.2s + s2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -1.2s + 3.2 + s2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -1.2s + s2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -1.2s + s2 = 0 + 3.2
-1.2s + s2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-1.2s + s2 = 3.2

The s term is -1.2s.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2s + 0.36 + s2 = 3.2 + 0.36

Reorder the terms:
0.36 + -1.2s + s2 = 3.2 + 0.36

Combine like terms: 3.2 + 0.36 = 3.56
0.36 + -1.2s + s2 = 3.56

Factor a perfect square on the left side:
(s + -0.6)(s + -0.6) = 3.56

Calculate the square root of the right side: 1.886796226

Break this problem into two subproblems by setting 
(s + -0.6) equal to 1.886796226 and -1.886796226.

Subproblem 1
s + -0.6 = 1.886796226

Simplifying
s + -0.6 = 1.886796226

Reorder the terms:
-0.6 + s = 1.886796226

Solving
-0.6 + s = 1.886796226

Solving for variable 's'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + s = 1.886796226 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + s = 1.886796226 + 0.6
s = 1.886796226 + 0.6

Combine like terms: 1.886796226 + 0.6 = 2.486796226
s = 2.486796226

Simplifying
s = 2.486796226

Subproblem 2
s + -0.6 = -1.886796226

Simplifying
s + -0.6 = -1.886796226

Reorder the terms:
-0.6 + s = -1.886796226

Solving
-0.6 + s = -1.886796226

Solving for variable 's'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + s = -1.886796226 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + s = -1.886796226 + 0.6
s = -1.886796226 + 0.6

Combine like terms: -1.886796226 + 0.6 = -1.286796226
s = -1.286796226

Simplifying
s = -1.286796226

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {2.486796226, -1.286796226}