8s^2-80s+30=-10

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Solution for 8s^2-80s+30=-10 equation: 


Simplifying
8s2 + -80s + 30 = -10

Reorder the terms:
30 + -80s + 8s2 = -10

Solving
30 + -80s + 8s2 = -10

Solving for variable 's'.

Reorder the terms:
30 + 10 + -80s + 8s2 = -10 + 10

Combine like terms: 30 + 10 = 40
40 + -80s + 8s2 = -10 + 10

Combine like terms: -10 + 10 = 0
40 + -80s + 8s2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + -10s + s2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(5 + -10s + s2)' equal to zero and attempt to solve:

Simplifying
5 + -10s + s2 = 0

Solving
5 + -10s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -10s + -5 + s2 = 0 + -5

Reorder the terms:
5 + -5 + -10s + s2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -10s + s2 = 0 + -5
-10s + s2 = 0 + -5

Combine like terms: 0 + -5 = -5
-10s + s2 = -5

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 = -5 + 25

Reorder the terms:
25 + -10s + s2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + -10s + s2 = 20

Factor a perfect square on the left side:
(s + -5)(s + -5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(s + -5) equal to 4.472135955 and -4.472135955.


Subproblem 1
s + -5 = 4.472135955

Simplifying
s + -5 = 4.472135955

Reorder the terms:
-5 + s = 4.472135955

Solving
-5 + s = 4.472135955

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 = 4.472135955 + 5

Combine like terms: -5 + 5 = 0
0 + s = 4.472135955 + 5
s = 4.472135955 + 5

Combine like terms: 4.472135955 + 5 = 9.472135955
s = 9.472135955

Simplifying
s = 9.472135955


Subproblem 2
s + -5 = -4.472135955

Simplifying
s + -5 = -4.472135955

Reorder the terms:
-5 + s = -4.472135955

Solving
-5 + s = -4.472135955

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 = -4.472135955 + 5

Combine like terms: -5 + 5 = 0
0 + s = -4.472135955 + 5
s = -4.472135955 + 5

Combine like terms: -4.472135955 + 5 = 0.527864045
s = 0.527864045

Simplifying
s = 0.527864045


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {9.472135955, 0.527864045}
Solution
s = {9.472135955, 0.527864045}

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