2s^2-20s-6=0

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Solution for 2s^2-20s-6=0 equation: 


Simplifying
2s2 + -20s + -6 = 0

Reorder the terms:
-6 + -20s + 2s2 = 0

Solving
-6 + -20s + 2s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -10s + s2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -10s + s2)' equal to zero and attempt to solve:

Simplifying
-3 + -10s + s2 = 0

Solving
-3 + -10s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -10s + 3 + s2 = 0 + 3

Reorder the terms:
-3 + 3 + -10s + s2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -10s + s2 = 0 + 3
-10s + s2 = 0 + 3

Combine like terms: 0 + 3 = 3
-10s + s2 = 3

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 = 3 + 25

Reorder the terms:
25 + -10s + s2 = 3 + 25

Combine like terms: 3 + 25 = 28
25 + -10s + s2 = 28

Factor a perfect square on the left side:
(s + -5)(s + -5) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(s + -5) equal to 5.291502622 and -5.291502622.


Subproblem 1
s + -5 = 5.291502622

Simplifying
s + -5 = 5.291502622

Reorder the terms:
-5 + s = 5.291502622

Solving
-5 + s = 5.291502622

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 = 5.291502622 + 5

Combine like terms: -5 + 5 = 0
0 + s = 5.291502622 + 5
s = 5.291502622 + 5

Combine like terms: 5.291502622 + 5 = 10.291502622
s = 10.291502622

Simplifying
s = 10.291502622


Subproblem 2
s + -5 = -5.291502622

Simplifying
s + -5 = -5.291502622

Reorder the terms:
-5 + s = -5.291502622

Solving
-5 + s = -5.291502622

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 = -5.291502622 + 5

Combine like terms: -5 + 5 = 0
0 + s = -5.291502622 + 5
s = -5.291502622 + 5

Combine like terms: -5.291502622 + 5 = -0.291502622
s = -0.291502622

Simplifying
s = -0.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {10.291502622, -0.291502622}
Solution
s = {10.291502622, -0.291502622}

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