3s^2-78s+33=0

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Solution for 3s^2-78s+33=0 equation: 


Simplifying
3s2 + -78s + 33 = 0

Reorder the terms:
33 + -78s + 3s2 = 0

Solving
33 + -78s + 3s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '3'.
3(11 + -26s + s2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(11 + -26s + s2)' equal to zero and attempt to solve:

Simplifying
11 + -26s + s2 = 0

Solving
11 + -26s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -26s + -11 + s2 = 0 + -11

Reorder the terms:
11 + -11 + -26s + s2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -26s + s2 = 0 + -11
-26s + s2 = 0 + -11

Combine like terms: 0 + -11 = -11
-26s + s2 = -11

The s term is -26s.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26s + 169 + s2 = -11 + 169

Reorder the terms:
169 + -26s + s2 = -11 + 169

Combine like terms: -11 + 169 = 158
169 + -26s + s2 = 158

Factor a perfect square on the left side:
(s + -13)(s + -13) = 158

Calculate the square root of the right side: 12.56980509

Break this problem into two subproblems by setting 
(s + -13) equal to 12.56980509 and -12.56980509.


Subproblem 1
s + -13 = 12.56980509

Simplifying
s + -13 = 12.56980509

Reorder the terms:
-13 + s = 12.56980509

Solving
-13 + s = 12.56980509

Solving for variable 's'.

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

Add '13' to each side of the equation.
-13 + 13 + s = 12.56980509 + 13

Combine like terms: -13 + 13 = 0
0 + s = 12.56980509 + 13
s = 12.56980509 + 13

Combine like terms: 12.56980509 + 13 = 25.56980509
s = 25.56980509

Simplifying
s = 25.56980509


Subproblem 2
s + -13 = -12.56980509

Simplifying
s + -13 = -12.56980509

Reorder the terms:
-13 + s = -12.56980509

Solving
-13 + s = -12.56980509

Solving for variable 's'.

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

Add '13' to each side of the equation.
-13 + 13 + s = -12.56980509 + 13

Combine like terms: -13 + 13 = 0
0 + s = -12.56980509 + 13
s = -12.56980509 + 13

Combine like terms: -12.56980509 + 13 = 0.43019491
s = 0.43019491

Simplifying
s = 0.43019491


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {25.56980509, 0.43019491}
Solution
s = {25.56980509, 0.43019491}

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