-4s^2-84s-184=0

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Solution for -4s^2-84s-184=0 equation: 


Simplifying
-4s2 + -84s + -184 = 0

Reorder the terms:
-184 + -84s + -4s2 = 0

Solving
-184 + -84s + -4s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(46 + 21s + s2) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(46 + 21s + s2)' equal to zero and attempt to solve:

Simplifying
46 + 21s + s2 = 0

Solving
46 + 21s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + 21s + -46 + s2 = 0 + -46

Reorder the terms:
46 + -46 + 21s + s2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + 21s + s2 = 0 + -46
21s + s2 = 0 + -46

Combine like terms: 0 + -46 = -46
21s + s2 = -46

The s term is 21s.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21s + 110.25 + s2 = -46 + 110.25

Reorder the terms:
110.25 + 21s + s2 = -46 + 110.25

Combine like terms: -46 + 110.25 = 64.25
110.25 + 21s + s2 = 64.25

Factor a perfect square on the left side:
(s + 10.5)(s + 10.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(s + 10.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
s + 10.5 = 8.015609771

Simplifying
s + 10.5 = 8.015609771

Reorder the terms:
10.5 + s = 8.015609771

Solving
10.5 + s = 8.015609771

Solving for variable 's'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + s = 8.015609771 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + s = 8.015609771 + -10.5
s = 8.015609771 + -10.5

Combine like terms: 8.015609771 + -10.5 = -2.484390229
s = -2.484390229

Simplifying
s = -2.484390229


Subproblem 2
s + 10.5 = -8.015609771

Simplifying
s + 10.5 = -8.015609771

Reorder the terms:
10.5 + s = -8.015609771

Solving
10.5 + s = -8.015609771

Solving for variable 's'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + s = -8.015609771 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + s = -8.015609771 + -10.5
s = -8.015609771 + -10.5

Combine like terms: -8.015609771 + -10.5 = -18.515609771
s = -18.515609771

Simplifying
s = -18.515609771


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-2.484390229, -18.515609771}
Solution
s = {-2.484390229, -18.515609771}

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