-3.8s^2+0.9s-1.8-3(9s^2+6.3s-3)=

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Solution for -3.8s^2+0.9s-1.8-3(9s^2+6.3s-3)= equation:


Simplifying
-3.8s2 + 0.9s + -1.8 + -3(9s2 + 6.3s + -3) = 0

Reorder the terms:
-3.8s2 + 0.9s + -1.8 + -3(-3 + 6.3s + 9s2) = 0
-3.8s2 + 0.9s + -1.8 + (-3 * -3 + 6.3s * -3 + 9s2 * -3) = 0
-3.8s2 + 0.9s + -1.8 + (9 + -18.9s + -27s2) = 0

Reorder the terms:
-1.8 + 9 + 0.9s + -18.9s + -3.8s2 + -27s2 = 0

Combine like terms: -1.8 + 9 = 7.2
7.2 + 0.9s + -18.9s + -3.8s2 + -27s2 = 0

Combine like terms: 0.9s + -18.9s = -18s
7.2 + -18s + -3.8s2 + -27s2 = 0

Combine like terms: -3.8s2 + -27s2 = -30.8s2
7.2 + -18s + -30.8s2 = 0

Solving
7.2 + -18s + -30.8s2 = 0

Solving for variable 's'.

Begin completing the square.  Divide all terms by
-30.8 the coefficient of the squared term: 

Divide each side by '-30.8'.
-0.2337662338 + 0.5844155844s + s2 = 0

Move the constant term to the right:

Add '0.2337662338' to each side of the equation.
-0.2337662338 + 0.5844155844s + 0.2337662338 + s2 = 0 + 0.2337662338

Reorder the terms:
-0.2337662338 + 0.2337662338 + 0.5844155844s + s2 = 0 + 0.2337662338

Combine like terms: -0.2337662338 + 0.2337662338 = 0.0000000000
0.0000000000 + 0.5844155844s + s2 = 0 + 0.2337662338
0.5844155844s + s2 = 0 + 0.2337662338

Combine like terms: 0 + 0.2337662338 = 0.2337662338
0.5844155844s + s2 = 0.2337662338

The s term is 0.5844155844s.  Take half its coefficient (0.2922077922).
Square it (0.08538539382) and add it to both sides.

Add '0.08538539382' to each side of the equation.
0.5844155844s + 0.08538539382 + s2 = 0.2337662338 + 0.08538539382

Reorder the terms:
0.08538539382 + 0.5844155844s + s2 = 0.2337662338 + 0.08538539382

Combine like terms: 0.2337662338 + 0.08538539382 = 0.31915162762
0.08538539382 + 0.5844155844s + s2 = 0.31915162762

Factor a perfect square on the left side:
(s + 0.2922077922)(s + 0.2922077922) = 0.31915162762

Calculate the square root of the right side: 0.564935065

Break this problem into two subproblems by setting 
(s + 0.2922077922) equal to 0.564935065 and -0.564935065.

Subproblem 1

s + 0.2922077922 = 0.564935065 Simplifying s + 0.2922077922 = 0.564935065 Reorder the terms: 0.2922077922 + s = 0.564935065 Solving 0.2922077922 + s = 0.564935065 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.2922077922' to each side of the equation. 0.2922077922 + -0.2922077922 + s = 0.564935065 + -0.2922077922 Combine like terms: 0.2922077922 + -0.2922077922 = 0.0000000000 0.0000000000 + s = 0.564935065 + -0.2922077922 s = 0.564935065 + -0.2922077922 Combine like terms: 0.564935065 + -0.2922077922 = 0.2727272728 s = 0.2727272728 Simplifying s = 0.2727272728

Subproblem 2

s + 0.2922077922 = -0.564935065 Simplifying s + 0.2922077922 = -0.564935065 Reorder the terms: 0.2922077922 + s = -0.564935065 Solving 0.2922077922 + s = -0.564935065 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.2922077922' to each side of the equation. 0.2922077922 + -0.2922077922 + s = -0.564935065 + -0.2922077922 Combine like terms: 0.2922077922 + -0.2922077922 = 0.0000000000 0.0000000000 + s = -0.564935065 + -0.2922077922 s = -0.564935065 + -0.2922077922 Combine like terms: -0.564935065 + -0.2922077922 = -0.8571428572 s = -0.8571428572 Simplifying s = -0.8571428572

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.2727272728, -0.8571428572}

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