s^2+8s-3=0

Solution for s^2+8s-3=0 equation:

Simplifying
s2 + 8s + -3 = 0

Reorder the terms:
-3 + 8s + s2 = 0

Solving
-3 + 8s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 8s + 3 + s2 = 0 + 3

Reorder the terms:
-3 + 3 + 8s + s2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 8s + s2 = 0 + 3
8s + s2 = 0 + 3

Combine like terms: 0 + 3 = 3
8s + s2 = 3

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

Add '16' to each side of the equation.
8s + 16 + s2 = 3 + 16

Reorder the terms:
16 + 8s + s2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + 8s + s2 = 19

Factor a perfect square on the left side:
(s + 4)(s + 4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(s + 4) equal to 4.358898944 and -4.358898944.

Subproblem 1
s + 4 = 4.358898944

Simplifying
s + 4 = 4.358898944

Reorder the terms:
4 + s = 4.358898944

Solving
4 + s = 4.358898944

Solving for variable 's'.

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

Add '-4' to each side of the equation.
4 + -4 + s = 4.358898944 + -4

Combine like terms: 4 + -4 = 0
0 + s = 4.358898944 + -4
s = 4.358898944 + -4

Combine like terms: 4.358898944 + -4 = 0.358898944
s = 0.358898944

Simplifying
s = 0.358898944

Subproblem 2
s + 4 = -4.358898944

Simplifying
s + 4 = -4.358898944

Reorder the terms:
4 + s = -4.358898944

Solving
4 + s = -4.358898944

Solving for variable 's'.

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

Add '-4' to each side of the equation.
4 + -4 + s = -4.358898944 + -4

Combine like terms: 4 + -4 = 0
0 + s = -4.358898944 + -4
s = -4.358898944 + -4

Combine like terms: -4.358898944 + -4 = -8.358898944
s = -8.358898944

Simplifying
s = -8.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.358898944, -8.358898944}