3s^2+15s-4+2s=

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Solution for 3s^2+15s-4+2s= equation: 


Simplifying
3s2 + 15s + -4 + 2s = 0

Reorder the terms:
-4 + 15s + 2s + 3s2 = 0

Combine like terms: 15s + 2s = 17s
-4 + 17s + 3s2 = 0

Solving
-4 + 17s + 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 + 5.666666667s + s2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 5.666666667s + 1.333333333 + s2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 5.666666667s + s2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 5.666666667s + s2 = 0 + 1.333333333
5.666666667s + s2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
5.666666667s + s2 = 1.333333333

The s term is 5.666666667s.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667s + 8.027777782 + s2 = 1.333333333 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667s + s2 = 1.333333333 + 8.027777782

Combine like terms: 1.333333333 + 8.027777782 = 9.361111115
8.027777782 + 5.666666667s + s2 = 9.361111115

Factor a perfect square on the left side:
(s + 2.833333334)(s + 2.833333334) = 9.361111115

Calculate the square root of the right side: 3.059593292

Break this problem into two subproblems by setting 
(s + 2.833333334) equal to 3.059593292 and -3.059593292.


Subproblem 1
s + 2.833333334 = 3.059593292

Simplifying
s + 2.833333334 = 3.059593292

Reorder the terms:
2.833333334 + s = 3.059593292

Solving
2.833333334 + s = 3.059593292

Solving for variable 's'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + s = 3.059593292 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + s = 3.059593292 + -2.833333334
s = 3.059593292 + -2.833333334

Combine like terms: 3.059593292 + -2.833333334 = 0.226259958
s = 0.226259958

Simplifying
s = 0.226259958


Subproblem 2
s + 2.833333334 = -3.059593292

Simplifying
s + 2.833333334 = -3.059593292

Reorder the terms:
2.833333334 + s = -3.059593292

Solving
2.833333334 + s = -3.059593292

Solving for variable 's'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + s = -3.059593292 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + s = -3.059593292 + -2.833333334
s = -3.059593292 + -2.833333334

Combine like terms: -3.059593292 + -2.833333334 = -5.892926626
s = -5.892926626

Simplifying
s = -5.892926626


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.226259958, -5.892926626}

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