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Simplifying 3s2 + 16s + 15 = 0 Reorder the terms: 15 + 16s + 3s2 = 0 Solving 15 + 16s + 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'. 5 + 5.333333333s + s2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5.333333333s + -5 + s2 = 0 + -5 Reorder the terms: 5 + -5 + 5.333333333s + s2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5.333333333s + s2 = 0 + -5 5.333333333s + s2 = 0 + -5 Combine like terms: 0 + -5 = -5 5.333333333s + s2 = -5 The s term is 5.333333333s. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333s + 7.111111113 + s2 = -5 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333s + s2 = -5 + 7.111111113 Combine like terms: -5 + 7.111111113 = 2.111111113 7.111111113 + 5.333333333s + s2 = 2.111111113 Factor a perfect square on the left side: (s + 2.666666667)(s + 2.666666667) = 2.111111113 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (s + 2.666666667) equal to 1.452966315 and -1.452966315.Subproblem 1
s + 2.666666667 = 1.452966315 Simplifying s + 2.666666667 = 1.452966315 Reorder the terms: 2.666666667 + s = 1.452966315 Solving 2.666666667 + s = 1.452966315 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + s = 1.452966315 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + s = 1.452966315 + -2.666666667 s = 1.452966315 + -2.666666667 Combine like terms: 1.452966315 + -2.666666667 = -1.213700352 s = -1.213700352 Simplifying s = -1.213700352Subproblem 2
s + 2.666666667 = -1.452966315 Simplifying s + 2.666666667 = -1.452966315 Reorder the terms: 2.666666667 + s = -1.452966315 Solving 2.666666667 + s = -1.452966315 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + s = -1.452966315 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + s = -1.452966315 + -2.666666667 s = -1.452966315 + -2.666666667 Combine like terms: -1.452966315 + -2.666666667 = -4.119632982 s = -4.119632982 Simplifying s = -4.119632982Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.213700352, -4.119632982}
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