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