s^2+6s+3=0

Solution for s^2+6s+3=0 equation:

Simplifying
s2 + 6s + 3 = 0

Reorder the terms:
3 + 6s + s2 = 0

Solving
3 + 6s + 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 + 6s + -3 + s2 = 0 + -3

Reorder the terms:
3 + -3 + 6s + s2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 6s + s2 = 0 + -3
6s + s2 = 0 + -3

Combine like terms: 0 + -3 = -3
6s + s2 = -3

The s term is 6s.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6s + 9 + s2 = -3 + 9

Reorder the terms:
9 + 6s + s2 = -3 + 9

Combine like terms: -3 + 9 = 6
9 + 6s + s2 = 6

Factor a perfect square on the left side:
(s + 3)(s + 3) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(s + 3) equal to 2.449489743 and -2.449489743.

Subproblem 1
s + 3 = 2.449489743

Simplifying
s + 3 = 2.449489743

Reorder the terms:
3 + s = 2.449489743

Solving
3 + s = 2.449489743

Solving for variable 's'.

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

Add '-3' to each side of the equation.
3 + -3 + s = 2.449489743 + -3

Combine like terms: 3 + -3 = 0
0 + s = 2.449489743 + -3
s = 2.449489743 + -3

Combine like terms: 2.449489743 + -3 = -0.550510257
s = -0.550510257

Simplifying
s = -0.550510257

Subproblem 2
s + 3 = -2.449489743

Simplifying
s + 3 = -2.449489743

Reorder the terms:
3 + s = -2.449489743

Solving
3 + s = -2.449489743

Solving for variable 's'.

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

Add '-3' to each side of the equation.
3 + -3 + s = -2.449489743 + -3

Combine like terms: 3 + -3 = 0
0 + s = -2.449489743 + -3
s = -2.449489743 + -3

Combine like terms: -2.449489743 + -3 = -5.449489743
s = -5.449489743

Simplifying
s = -5.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.550510257, -5.449489743}