s^2+20s+2=0

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Solution for s^2+20s+2=0 equation: 


Simplifying
s2 + 20s + 2 = 0

Reorder the terms:
2 + 20s + s2 = 0

Solving
2 + 20s + 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 + 20s + -2 + s2 = 0 + -2

Reorder the terms:
2 + -2 + 20s + s2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 20s + s2 = 0 + -2
20s + s2 = 0 + -2

Combine like terms: 0 + -2 = -2
20s + s2 = -2

The s term is 20s.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20s + 100 + s2 = -2 + 100

Reorder the terms:
100 + 20s + s2 = -2 + 100

Combine like terms: -2 + 100 = 98
100 + 20s + s2 = 98

Factor a perfect square on the left side:
(s + 10)(s + 10) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(s + 10) equal to 9.899494937 and -9.899494937.


Subproblem 1
s + 10 = 9.899494937

Simplifying
s + 10 = 9.899494937

Reorder the terms:
10 + s = 9.899494937

Solving
10 + s = 9.899494937

Solving for variable 's'.

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

Add '-10' to each side of the equation.
10 + -10 + s = 9.899494937 + -10

Combine like terms: 10 + -10 = 0
0 + s = 9.899494937 + -10
s = 9.899494937 + -10

Combine like terms: 9.899494937 + -10 = -0.100505063
s = -0.100505063

Simplifying
s = -0.100505063


Subproblem 2
s + 10 = -9.899494937

Simplifying
s + 10 = -9.899494937

Reorder the terms:
10 + s = -9.899494937

Solving
10 + s = -9.899494937

Solving for variable 's'.

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

Add '-10' to each side of the equation.
10 + -10 + s = -9.899494937 + -10

Combine like terms: 10 + -10 = 0
0 + s = -9.899494937 + -10
s = -9.899494937 + -10

Combine like terms: -9.899494937 + -10 = -19.899494937
s = -19.899494937

Simplifying
s = -19.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.100505063, -19.899494937}

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