-25s^2-20s-2=0

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Solution for -25s^2-20s-2=0 equation: 


Simplifying
-25s2 + -20s + -2 = 0

Reorder the terms:
-2 + -20s + -25s2 = 0

Solving
-2 + -20s + -25s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 20s + 25s2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 20s + 25s2)' equal to zero and attempt to solve:

Simplifying
2 + 20s + 25s2 = 0

Solving
2 + 20s + 25s2 = 0

Begin completing the square.  Divide all terms by
25 the coefficient of the squared term: 

Divide each side by '25'.
0.08 + 0.8s + s2 = 0

Move the constant term to the right:

Add '-0.08' to each side of the equation.
0.08 + 0.8s + -0.08 + s2 = 0 + -0.08

Reorder the terms:
0.08 + -0.08 + 0.8s + s2 = 0 + -0.08

Combine like terms: 0.08 + -0.08 = 0.00
0.00 + 0.8s + s2 = 0 + -0.08
0.8s + s2 = 0 + -0.08

Combine like terms: 0 + -0.08 = -0.08
0.8s + s2 = -0.08

The s term is 0.8s.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8s + 0.16 + s2 = -0.08 + 0.16

Reorder the terms:
0.16 + 0.8s + s2 = -0.08 + 0.16

Combine like terms: -0.08 + 0.16 = 0.08
0.16 + 0.8s + s2 = 0.08

Factor a perfect square on the left side:
(s + 0.4)(s + 0.4) = 0.08

Calculate the square root of the right side: 0.282842712

Break this problem into two subproblems by setting 
(s + 0.4) equal to 0.282842712 and -0.282842712.


Subproblem 1
s + 0.4 = 0.282842712

Simplifying
s + 0.4 = 0.282842712

Reorder the terms:
0.4 + s = 0.282842712

Solving
0.4 + s = 0.282842712

Solving for variable 's'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + s = 0.282842712 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + s = 0.282842712 + -0.4
s = 0.282842712 + -0.4

Combine like terms: 0.282842712 + -0.4 = -0.117157288
s = -0.117157288

Simplifying
s = -0.117157288


Subproblem 2
s + 0.4 = -0.282842712

Simplifying
s + 0.4 = -0.282842712

Reorder the terms:
0.4 + s = -0.282842712

Solving
0.4 + s = -0.282842712

Solving for variable 's'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + s = -0.282842712 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + s = -0.282842712 + -0.4
s = -0.282842712 + -0.4

Combine like terms: -0.282842712 + -0.4 = -0.682842712
s = -0.682842712

Simplifying
s = -0.682842712


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.117157288, -0.682842712}
Solution
s = {-0.117157288, -0.682842712}

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