s^2+5s+3=0

Solution for s^2+5s+3=0 equation:

Simplifying
s2 + 5s + 3 = 0

Reorder the terms:
3 + 5s + s2 = 0

Solving
3 + 5s + 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 + 5s + -3 + s2 = 0 + -3

Reorder the terms:
3 + -3 + 5s + s2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5s + s2 = 0 + -3
5s + s2 = 0 + -3

Combine like terms: 0 + -3 = -3
5s + s2 = -3

The s term is 5s.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5s + 6.25 + s2 = -3 + 6.25

Reorder the terms:
6.25 + 5s + s2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + 5s + s2 = 3.25

Factor a perfect square on the left side:
(s + 2.5)(s + 2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(s + 2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
s + 2.5 = 1.802775638

Simplifying
s + 2.5 = 1.802775638

Reorder the terms:
2.5 + s = 1.802775638

Solving
2.5 + s = 1.802775638

Solving for variable 's'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + s = 1.802775638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + s = 1.802775638 + -2.5
s = 1.802775638 + -2.5

Combine like terms: 1.802775638 + -2.5 = -0.697224362
s = -0.697224362

Simplifying
s = -0.697224362

Subproblem 2
s + 2.5 = -1.802775638

Simplifying
s + 2.5 = -1.802775638

Reorder the terms:
2.5 + s = -1.802775638

Solving
2.5 + s = -1.802775638

Solving for variable 's'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + s = -1.802775638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + s = -1.802775638 + -2.5
s = -1.802775638 + -2.5

Combine like terms: -1.802775638 + -2.5 = -4.302775638
s = -4.302775638

Simplifying
s = -4.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.697224362, -4.302775638}