3s^2+30s+54=0

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Solution for 3s^2+30s+54=0 equation: 


Simplifying
3s2 + 30s + 54 = 0

Reorder the terms:
54 + 30s + 3s2 = 0

Solving
54 + 30s + 3s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + 10s + s2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(18 + 10s + s2)' equal to zero and attempt to solve:

Simplifying
18 + 10s + s2 = 0

Solving
18 + 10s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 10s + -18 + s2 = 0 + -18

Reorder the terms:
18 + -18 + 10s + s2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 10s + s2 = 0 + -18
10s + s2 = 0 + -18

Combine like terms: 0 + -18 = -18
10s + s2 = -18

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 = -18 + 25

Reorder the terms:
25 + 10s + s2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + 10s + s2 = 7

Factor a perfect square on the left side:
(s + 5)(s + 5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(s + 5) equal to 2.645751311 and -2.645751311.


Subproblem 1
s + 5 = 2.645751311

Simplifying
s + 5 = 2.645751311

Reorder the terms:
5 + s = 2.645751311

Solving
5 + s = 2.645751311

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 = 2.645751311 + -5

Combine like terms: 5 + -5 = 0
0 + s = 2.645751311 + -5
s = 2.645751311 + -5

Combine like terms: 2.645751311 + -5 = -2.354248689
s = -2.354248689

Simplifying
s = -2.354248689


Subproblem 2
s + 5 = -2.645751311

Simplifying
s + 5 = -2.645751311

Reorder the terms:
5 + s = -2.645751311

Solving
5 + s = -2.645751311

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 = -2.645751311 + -5

Combine like terms: 5 + -5 = 0
0 + s = -2.645751311 + -5
s = -2.645751311 + -5

Combine like terms: -2.645751311 + -5 = -7.645751311
s = -7.645751311

Simplifying
s = -7.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-2.354248689, -7.645751311}
Solution
s = {-2.354248689, -7.645751311}

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