3s^2-11s+4=0

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Solution for 3s^2-11s+4=0 equation:


Simplifying
3s2 + -11s + 4 = 0

Reorder the terms:
4 + -11s + 3s2 = 0

Solving
4 + -11s + 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'.
1.333333333 + -3.666666667s + s2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -3.666666667s + -1.333333333 + s2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -3.666666667s + s2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -3.666666667s + s2 = 0 + -1.333333333
-3.666666667s + s2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-3.666666667s + s2 = -1.333333333

The s term is -3.666666667s.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667s + 3.361111114 + s2 = -1.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667s + s2 = -1.333333333 + 3.361111114

Combine like terms: -1.333333333 + 3.361111114 = 2.027777781
3.361111114 + -3.666666667s + s2 = 2.027777781

Factor a perfect square on the left side:
(s + -1.833333334)(s + -1.833333334) = 2.027777781

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(s + -1.833333334) equal to 1.424000625 and -1.424000625.

Subproblem 1

s + -1.833333334 = 1.424000625 Simplifying s + -1.833333334 = 1.424000625 Reorder the terms: -1.833333334 + s = 1.424000625 Solving -1.833333334 + s = 1.424000625 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + s = 1.424000625 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + s = 1.424000625 + 1.833333334 s = 1.424000625 + 1.833333334 Combine like terms: 1.424000625 + 1.833333334 = 3.257333959 s = 3.257333959 Simplifying s = 3.257333959

Subproblem 2

s + -1.833333334 = -1.424000625 Simplifying s + -1.833333334 = -1.424000625 Reorder the terms: -1.833333334 + s = -1.424000625 Solving -1.833333334 + s = -1.424000625 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + s = -1.424000625 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + s = -1.424000625 + 1.833333334 s = -1.424000625 + 1.833333334 Combine like terms: -1.424000625 + 1.833333334 = 0.409332709 s = 0.409332709 Simplifying s = 0.409332709

Solution

The solution to the problem is based on the solutions from the subproblems. s = {3.257333959, 0.409332709}

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