3s^2+30s+50=0

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Solution for 3s^2+30s+50=0 equation: 


Simplifying
3s2 + 30s + 50 = 0

Reorder the terms:
50 + 30s + 3s2 = 0

Solving
50 + 30s + 3s2 = 0

Solving for variable 's'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
16.66666667 + 10s + s2 = 0

Move the constant term to the right:

Add '-16.66666667' to each side of the equation.
16.66666667 + 10s + -16.66666667 + s2 = 0 + -16.66666667

Reorder the terms:
16.66666667 + -16.66666667 + 10s + s2 = 0 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + 10s + s2 = 0 + -16.66666667
10s + s2 = 0 + -16.66666667

Combine like terms: 0 + -16.66666667 = -16.66666667
10s + s2 = -16.66666667

The s term is 10s.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10s + 25 + s2 = -16.66666667 + 25

Reorder the terms:
25 + 10s + s2 = -16.66666667 + 25

Combine like terms: -16.66666667 + 25 = 8.33333333
25 + 10s + s2 = 8.33333333

Factor a perfect square on the left side:
(s + 5)(s + 5) = 8.33333333

Calculate the square root of the right side: 2.886751345

Break this problem into two subproblems by setting 
(s + 5) equal to 2.886751345 and -2.886751345.


Subproblem 1
s + 5 = 2.886751345

Simplifying
s + 5 = 2.886751345

Reorder the terms:
5 + s = 2.886751345

Solving
5 + s = 2.886751345

Solving for variable 's'.

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

Add '-5' to each side of the equation.
5 + -5 + s = 2.886751345 + -5

Combine like terms: 5 + -5 = 0
0 + s = 2.886751345 + -5
s = 2.886751345 + -5

Combine like terms: 2.886751345 + -5 = -2.113248655
s = -2.113248655

Simplifying
s = -2.113248655


Subproblem 2
s + 5 = -2.886751345

Simplifying
s + 5 = -2.886751345

Reorder the terms:
5 + s = -2.886751345

Solving
5 + s = -2.886751345

Solving for variable 's'.

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

Add '-5' to each side of the equation.
5 + -5 + s = -2.886751345 + -5

Combine like terms: 5 + -5 = 0
0 + s = -2.886751345 + -5
s = -2.886751345 + -5

Combine like terms: -2.886751345 + -5 = -7.886751345
s = -7.886751345

Simplifying
s = -7.886751345


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-2.113248655, -7.886751345}

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