s^2+8s+2=0

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

Simplifying
s2 + 8s + 2 = 0

Reorder the terms:
2 + 8s + s2 = 0

Solving
2 + 8s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 8s + -2 + s2 = 0 + -2

Reorder the terms:
2 + -2 + 8s + s2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 8s + s2 = 0 + -2
8s + s2 = 0 + -2

Combine like terms: 0 + -2 = -2
8s + s2 = -2

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 = -2 + 16

Reorder the terms:
16 + 8s + s2 = -2 + 16

Combine like terms: -2 + 16 = 14
16 + 8s + s2 = 14

Factor a perfect square on the left side:
(s + 4)(s + 4) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(s + 4) equal to 3.741657387 and -3.741657387.

Subproblem 1
s + 4 = 3.741657387

Simplifying
s + 4 = 3.741657387

Reorder the terms:
4 + s = 3.741657387

Solving
4 + s = 3.741657387

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 = 3.741657387 + -4

Combine like terms: 4 + -4 = 0
0 + s = 3.741657387 + -4
s = 3.741657387 + -4

Combine like terms: 3.741657387 + -4 = -0.258342613
s = -0.258342613

Simplifying
s = -0.258342613

Subproblem 2
s + 4 = -3.741657387

Simplifying
s + 4 = -3.741657387

Reorder the terms:
4 + s = -3.741657387

Solving
4 + s = -3.741657387

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 = -3.741657387 + -4

Combine like terms: 4 + -4 = 0
0 + s = -3.741657387 + -4
s = -3.741657387 + -4

Combine like terms: -3.741657387 + -4 = -7.741657387
s = -7.741657387

Simplifying
s = -7.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.258342613, -7.741657387}