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Simplifying 3s2 + 8s + -360 = 0 Reorder the terms: -360 + 8s + 3s2 = 0 Solving -360 + 8s + 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'. -120 + 2.666666667s + s2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 2.666666667s + 120 + s2 = 0 + 120 Reorder the terms: -120 + 120 + 2.666666667s + s2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 2.666666667s + s2 = 0 + 120 2.666666667s + s2 = 0 + 120 Combine like terms: 0 + 120 = 120 2.666666667s + s2 = 120 The s term is 2.666666667s. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667s + 1.777777780 + s2 = 120 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667s + s2 = 120 + 1.777777780 Combine like terms: 120 + 1.777777780 = 121.77777778 1.777777780 + 2.666666667s + s2 = 121.77777778 Factor a perfect square on the left side: (s + 1.333333334)(s + 1.333333334) = 121.77777778 Calculate the square root of the right side: 11.035296905 Break this problem into two subproblems by setting (s + 1.333333334) equal to 11.035296905 and -11.035296905.Subproblem 1
s + 1.333333334 = 11.035296905 Simplifying s + 1.333333334 = 11.035296905 Reorder the terms: 1.333333334 + s = 11.035296905 Solving 1.333333334 + s = 11.035296905 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + s = 11.035296905 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + s = 11.035296905 + -1.333333334 s = 11.035296905 + -1.333333334 Combine like terms: 11.035296905 + -1.333333334 = 9.701963571 s = 9.701963571 Simplifying s = 9.701963571Subproblem 2
s + 1.333333334 = -11.035296905 Simplifying s + 1.333333334 = -11.035296905 Reorder the terms: 1.333333334 + s = -11.035296905 Solving 1.333333334 + s = -11.035296905 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + s = -11.035296905 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + s = -11.035296905 + -1.333333334 s = -11.035296905 + -1.333333334 Combine like terms: -11.035296905 + -1.333333334 = -12.368630239 s = -12.368630239 Simplifying s = -12.368630239Solution
The solution to the problem is based on the solutions from the subproblems. s = {9.701963571, -12.368630239}
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