4s^2+56s+116=0

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Solution for 4s^2+56s+116=0 equation: 


Simplifying
4s2 + 56s + 116 = 0

Reorder the terms:
116 + 56s + 4s2 = 0

Solving
116 + 56s + 4s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '4'.
4(29 + 14s + s2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(29 + 14s + s2)' equal to zero and attempt to solve:

Simplifying
29 + 14s + s2 = 0

Solving
29 + 14s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + 14s + -29 + s2 = 0 + -29

Reorder the terms:
29 + -29 + 14s + s2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 14s + s2 = 0 + -29
14s + s2 = 0 + -29

Combine like terms: 0 + -29 = -29
14s + s2 = -29

The s term is 14s.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14s + 49 + s2 = -29 + 49

Reorder the terms:
49 + 14s + s2 = -29 + 49

Combine like terms: -29 + 49 = 20
49 + 14s + s2 = 20

Factor a perfect square on the left side:
(s + 7)(s + 7) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(s + 7) equal to 4.472135955 and -4.472135955.


Subproblem 1
s + 7 = 4.472135955

Simplifying
s + 7 = 4.472135955

Reorder the terms:
7 + s = 4.472135955

Solving
7 + s = 4.472135955

Solving for variable 's'.

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

Add '-7' to each side of the equation.
7 + -7 + s = 4.472135955 + -7

Combine like terms: 7 + -7 = 0
0 + s = 4.472135955 + -7
s = 4.472135955 + -7

Combine like terms: 4.472135955 + -7 = -2.527864045
s = -2.527864045

Simplifying
s = -2.527864045


Subproblem 2
s + 7 = -4.472135955

Simplifying
s + 7 = -4.472135955

Reorder the terms:
7 + s = -4.472135955

Solving
7 + s = -4.472135955

Solving for variable 's'.

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

Add '-7' to each side of the equation.
7 + -7 + s = -4.472135955 + -7

Combine like terms: 7 + -7 = 0
0 + s = -4.472135955 + -7
s = -4.472135955 + -7

Combine like terms: -4.472135955 + -7 = -11.472135955
s = -11.472135955

Simplifying
s = -11.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-2.527864045, -11.472135955}
Solution
s = {-2.527864045, -11.472135955}

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