S^2+20S+5=0

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Solution for S^2+20S+5=0 equation: 


Simplifying
S2 + 20S + 5 = 0

Reorder the terms:
5 + 20S + S2 = 0

Solving
5 + 20S + S2 = 0

Solving for variable 'S'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 20S + -5 + S2 = 0 + -5

Reorder the terms:
5 + -5 + 20S + S2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 20S + S2 = 0 + -5
20S + S2 = 0 + -5

Combine like terms: 0 + -5 = -5
20S + S2 = -5

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 = -5 + 100

Reorder the terms:
100 + 20S + S2 = -5 + 100

Combine like terms: -5 + 100 = 95
100 + 20S + S2 = 95

Factor a perfect square on the left side:
(S + 10)(S + 10) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(S + 10) equal to 9.746794345 and -9.746794345.


Subproblem 1
S + 10 = 9.746794345

Simplifying
S + 10 = 9.746794345

Reorder the terms:
10 + S = 9.746794345

Solving
10 + S = 9.746794345

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 = 9.746794345 + -10

Combine like terms: 10 + -10 = 0
0 + S = 9.746794345 + -10
S = 9.746794345 + -10

Combine like terms: 9.746794345 + -10 = -0.253205655
S = -0.253205655

Simplifying
S = -0.253205655


Subproblem 2
S + 10 = -9.746794345

Simplifying
S + 10 = -9.746794345

Reorder the terms:
10 + S = -9.746794345

Solving
10 + S = -9.746794345

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 = -9.746794345 + -10

Combine like terms: 10 + -10 = 0
0 + S = -9.746794345 + -10
S = -9.746794345 + -10

Combine like terms: -9.746794345 + -10 = -19.746794345
S = -19.746794345

Simplifying
S = -19.746794345


Solution
The solution to the problem is based on the solutions
from the subproblems.
S = {-0.253205655, -19.746794345}

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