6s^2-70s+49=0

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Solution for 6s^2-70s+49=0 equation: 


Simplifying
6s2 + -70s + 49 = 0

Reorder the terms:
49 + -70s + 6s2 = 0

Solving
49 + -70s + 6s2 = 0

Solving for variable 's'.

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

Divide each side by '6'.
8.166666667 + -11.66666667s + s2 = 0

Move the constant term to the right:

Add '-8.166666667' to each side of the equation.
8.166666667 + -11.66666667s + -8.166666667 + s2 = 0 + -8.166666667

Reorder the terms:
8.166666667 + -8.166666667 + -11.66666667s + s2 = 0 + -8.166666667

Combine like terms: 8.166666667 + -8.166666667 = 0.000000000
0.000000000 + -11.66666667s + s2 = 0 + -8.166666667
-11.66666667s + s2 = 0 + -8.166666667

Combine like terms: 0 + -8.166666667 = -8.166666667
-11.66666667s + s2 = -8.166666667

The s term is -11.66666667s.  Take half its coefficient (-5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
-11.66666667s + 34.02777780 + s2 = -8.166666667 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667s + s2 = -8.166666667 + 34.02777780

Combine like terms: -8.166666667 + 34.02777780 = 25.861111133
34.02777780 + -11.66666667s + s2 = 25.861111133

Factor a perfect square on the left side:
(s + -5.833333335)(s + -5.833333335) = 25.861111133

Calculate the square root of the right side: 5.085382103

Break this problem into two subproblems by setting 
(s + -5.833333335) equal to 5.085382103 and -5.085382103.


Subproblem 1
s + -5.833333335 = 5.085382103

Simplifying
s + -5.833333335 = 5.085382103

Reorder the terms:
-5.833333335 + s = 5.085382103

Solving
-5.833333335 + s = 5.085382103

Solving for variable 's'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + s = 5.085382103 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + s = 5.085382103 + 5.833333335
s = 5.085382103 + 5.833333335

Combine like terms: 5.085382103 + 5.833333335 = 10.918715438
s = 10.918715438

Simplifying
s = 10.918715438


Subproblem 2
s + -5.833333335 = -5.085382103

Simplifying
s + -5.833333335 = -5.085382103

Reorder the terms:
-5.833333335 + s = -5.085382103

Solving
-5.833333335 + s = -5.085382103

Solving for variable 's'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + s = -5.085382103 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + s = -5.085382103 + 5.833333335
s = -5.085382103 + 5.833333335

Combine like terms: -5.085382103 + 5.833333335 = 0.747951232
s = 0.747951232

Simplifying
s = 0.747951232


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {10.918715438, 0.747951232}

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