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 = 13
16 + 8s + s2 = 13

Factor a perfect square on the left side:
(s + 4)(s + 4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(s + 4) equal to 3.605551275 and -3.605551275.

Subproblem 1
s + 4 = 3.605551275

Simplifying
s + 4 = 3.605551275

Reorder the terms:
4 + s = 3.605551275

Solving
4 + s = 3.605551275

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 = 3.605551275 + -4

Combine like terms: 4 + -4 = 0
0 + s = 3.605551275 + -4
s = 3.605551275 + -4

Combine like terms: 3.605551275 + -4 = -0.394448725
s = -0.394448725

Simplifying
s = -0.394448725

Subproblem 2
s + 4 = -3.605551275

Simplifying
s + 4 = -3.605551275

Reorder the terms:
4 + s = -3.605551275

Solving
4 + s = -3.605551275

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 = -3.605551275 + -4

Combine like terms: 4 + -4 = 0
0 + s = -3.605551275 + -4
s = -3.605551275 + -4

Combine like terms: -3.605551275 + -4 = -7.605551275
s = -7.605551275

Simplifying
s = -7.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.394448725, -7.605551275}