3s^2-23s+5=

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Solution for 3s^2-23s+5= equation: 


Simplifying
3s2 + -23s + 5 = 0

Reorder the terms:
5 + -23s + 3s2 = 0

Solving
5 + -23s + 3s2 = 0

Solving for variable 's'.

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

Divide each side by '3'.
1.666666667 + -7.666666667s + s2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -7.666666667s + -1.666666667 + s2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -7.666666667s + s2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -7.666666667s + s2 = 0 + -1.666666667
-7.666666667s + s2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-7.666666667s + s2 = -1.666666667

The s term is -7.666666667s.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667s + 14.69444445 + s2 = -1.666666667 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667s + s2 = -1.666666667 + 14.69444445

Combine like terms: -1.666666667 + 14.69444445 = 13.027777783
14.69444445 + -7.666666667s + s2 = 13.027777783

Factor a perfect square on the left side:
(s + -3.833333334)(s + -3.833333334) = 13.027777783

Calculate the square root of the right side: 3.609401305

Break this problem into two subproblems by setting 
(s + -3.833333334) equal to 3.609401305 and -3.609401305.


Subproblem 1
s + -3.833333334 = 3.609401305

Simplifying
s + -3.833333334 = 3.609401305

Reorder the terms:
-3.833333334 + s = 3.609401305

Solving
-3.833333334 + s = 3.609401305

Solving for variable 's'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + s = 3.609401305 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + s = 3.609401305 + 3.833333334
s = 3.609401305 + 3.833333334

Combine like terms: 3.609401305 + 3.833333334 = 7.442734639
s = 7.442734639

Simplifying
s = 7.442734639


Subproblem 2
s + -3.833333334 = -3.609401305

Simplifying
s + -3.833333334 = -3.609401305

Reorder the terms:
-3.833333334 + s = -3.609401305

Solving
-3.833333334 + s = -3.609401305

Solving for variable 's'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + s = -3.609401305 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + s = -3.609401305 + 3.833333334
s = -3.609401305 + 3.833333334

Combine like terms: -3.609401305 + 3.833333334 = 0.223932029
s = 0.223932029

Simplifying
s = 0.223932029


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {7.442734639, 0.223932029}

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