2s^2+98s-120=0

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Solution for 2s^2+98s-120=0 equation: 


Simplifying
2s2 + 98s + -120 = 0

Reorder the terms:
-120 + 98s + 2s2 = 0

Solving
-120 + 98s + 2s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 49s + s2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-60 + 49s + s2)' equal to zero and attempt to solve:

Simplifying
-60 + 49s + s2 = 0

Solving
-60 + 49s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 49s + 60 + s2 = 0 + 60

Reorder the terms:
-60 + 60 + 49s + s2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 49s + s2 = 0 + 60
49s + s2 = 0 + 60

Combine like terms: 0 + 60 = 60
49s + s2 = 60

The s term is 49s.  Take half its coefficient (24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
49s + 600.25 + s2 = 60 + 600.25

Reorder the terms:
600.25 + 49s + s2 = 60 + 600.25

Combine like terms: 60 + 600.25 = 660.25
600.25 + 49s + s2 = 660.25

Factor a perfect square on the left side:
(s + 24.5)(s + 24.5) = 660.25

Calculate the square root of the right side: 25.695330315

Break this problem into two subproblems by setting 
(s + 24.5) equal to 25.695330315 and -25.695330315.


Subproblem 1
s + 24.5 = 25.695330315

Simplifying
s + 24.5 = 25.695330315

Reorder the terms:
24.5 + s = 25.695330315

Solving
24.5 + s = 25.695330315

Solving for variable 's'.

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

Add '-24.5' to each side of the equation.
24.5 + -24.5 + s = 25.695330315 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
0.0 + s = 25.695330315 + -24.5
s = 25.695330315 + -24.5

Combine like terms: 25.695330315 + -24.5 = 1.195330315
s = 1.195330315

Simplifying
s = 1.195330315


Subproblem 2
s + 24.5 = -25.695330315

Simplifying
s + 24.5 = -25.695330315

Reorder the terms:
24.5 + s = -25.695330315

Solving
24.5 + s = -25.695330315

Solving for variable 's'.

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

Add '-24.5' to each side of the equation.
24.5 + -24.5 + s = -25.695330315 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
0.0 + s = -25.695330315 + -24.5
s = -25.695330315 + -24.5

Combine like terms: -25.695330315 + -24.5 = -50.195330315
s = -50.195330315

Simplifying
s = -50.195330315


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {1.195330315, -50.195330315}
Solution
s = {1.195330315, -50.195330315}

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