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Simplifying 3.6 = 9.5t + -4.9t2 Solving 3.6 = 9.5t + -4.9t2 Solving for variable 't'. Reorder the terms: 3.6 + -9.5t + 4.9t2 = 9.5t + -9.5t + -4.9t2 + 4.9t2 Combine like terms: 9.5t + -9.5t = 0.0 3.6 + -9.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 3.6 + -9.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 3.6 + -9.5t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.7346938776 + -1.93877551t + t2 = 0 Move the constant term to the right: Add '-0.7346938776' to each side of the equation. 0.7346938776 + -1.93877551t + -0.7346938776 + t2 = 0 + -0.7346938776 Reorder the terms: 0.7346938776 + -0.7346938776 + -1.93877551t + t2 = 0 + -0.7346938776 Combine like terms: 0.7346938776 + -0.7346938776 = 0.0000000000 0.0000000000 + -1.93877551t + t2 = 0 + -0.7346938776 -1.93877551t + t2 = 0 + -0.7346938776 Combine like terms: 0 + -0.7346938776 = -0.7346938776 -1.93877551t + t2 = -0.7346938776 The t term is -1.93877551t. Take half its coefficient (-0.969387755). Square it (0.9397126195) and add it to both sides. Add '0.9397126195' to each side of the equation. -1.93877551t + 0.9397126195 + t2 = -0.7346938776 + 0.9397126195 Reorder the terms: 0.9397126195 + -1.93877551t + t2 = -0.7346938776 + 0.9397126195 Combine like terms: -0.7346938776 + 0.9397126195 = 0.2050187419 0.9397126195 + -1.93877551t + t2 = 0.2050187419 Factor a perfect square on the left side: (t + -0.969387755)(t + -0.969387755) = 0.2050187419 Calculate the square root of the right side: 0.452789953 Break this problem into two subproblems by setting (t + -0.969387755) equal to 0.452789953 and -0.452789953.Subproblem 1
t + -0.969387755 = 0.452789953 Simplifying t + -0.969387755 = 0.452789953 Reorder the terms: -0.969387755 + t = 0.452789953 Solving -0.969387755 + t = 0.452789953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.969387755' to each side of the equation. -0.969387755 + 0.969387755 + t = 0.452789953 + 0.969387755 Combine like terms: -0.969387755 + 0.969387755 = 0.000000000 0.000000000 + t = 0.452789953 + 0.969387755 t = 0.452789953 + 0.969387755 Combine like terms: 0.452789953 + 0.969387755 = 1.422177708 t = 1.422177708 Simplifying t = 1.422177708Subproblem 2
t + -0.969387755 = -0.452789953 Simplifying t + -0.969387755 = -0.452789953 Reorder the terms: -0.969387755 + t = -0.452789953 Solving -0.969387755 + t = -0.452789953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.969387755' to each side of the equation. -0.969387755 + 0.969387755 + t = -0.452789953 + 0.969387755 Combine like terms: -0.969387755 + 0.969387755 = 0.000000000 0.000000000 + t = -0.452789953 + 0.969387755 t = -0.452789953 + 0.969387755 Combine like terms: -0.452789953 + 0.969387755 = 0.516597802 t = 0.516597802 Simplifying t = 0.516597802Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.422177708, 0.516597802}
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