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Simplifying -2 = -1.85(t2) + 10t Reorder the terms: -2 = 10t + -1.85t2 Solving -2 = 10t + -1.85t2 Solving for variable 't'. Reorder the terms: -2 + -10t + 1.85t2 = 10t + -10t + -1.85t2 + 1.85t2 Combine like terms: 10t + -10t = 0 -2 + -10t + 1.85t2 = 0 + -1.85t2 + 1.85t2 -2 + -10t + 1.85t2 = -1.85t2 + 1.85t2 Combine like terms: -1.85t2 + 1.85t2 = 0.00 -2 + -10t + 1.85t2 = 0.00 Begin completing the square. Divide all terms by 1.85 the coefficient of the squared term: Divide each side by '1.85'. -1.081081081 + -5.405405405t + t2 = 0 Move the constant term to the right: Add '1.081081081' to each side of the equation. -1.081081081 + -5.405405405t + 1.081081081 + t2 = 0 + 1.081081081 Reorder the terms: -1.081081081 + 1.081081081 + -5.405405405t + t2 = 0 + 1.081081081 Combine like terms: -1.081081081 + 1.081081081 = 0.000000000 0.000000000 + -5.405405405t + t2 = 0 + 1.081081081 -5.405405405t + t2 = 0 + 1.081081081 Combine like terms: 0 + 1.081081081 = 1.081081081 -5.405405405t + t2 = 1.081081081 The t term is -5.405405405t. Take half its coefficient (-2.702702703). Square it (7.304601901) and add it to both sides. Add '7.304601901' to each side of the equation. -5.405405405t + 7.304601901 + t2 = 1.081081081 + 7.304601901 Reorder the terms: 7.304601901 + -5.405405405t + t2 = 1.081081081 + 7.304601901 Combine like terms: 1.081081081 + 7.304601901 = 8.385682982 7.304601901 + -5.405405405t + t2 = 8.385682982 Factor a perfect square on the left side: (t + -2.702702703)(t + -2.702702703) = 8.385682982 Calculate the square root of the right side: 2.895804376 Break this problem into two subproblems by setting (t + -2.702702703) equal to 2.895804376 and -2.895804376.Subproblem 1
t + -2.702702703 = 2.895804376 Simplifying t + -2.702702703 = 2.895804376 Reorder the terms: -2.702702703 + t = 2.895804376 Solving -2.702702703 + t = 2.895804376 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.702702703' to each side of the equation. -2.702702703 + 2.702702703 + t = 2.895804376 + 2.702702703 Combine like terms: -2.702702703 + 2.702702703 = 0.000000000 0.000000000 + t = 2.895804376 + 2.702702703 t = 2.895804376 + 2.702702703 Combine like terms: 2.895804376 + 2.702702703 = 5.598507079 t = 5.598507079 Simplifying t = 5.598507079Subproblem 2
t + -2.702702703 = -2.895804376 Simplifying t + -2.702702703 = -2.895804376 Reorder the terms: -2.702702703 + t = -2.895804376 Solving -2.702702703 + t = -2.895804376 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.702702703' to each side of the equation. -2.702702703 + 2.702702703 + t = -2.895804376 + 2.702702703 Combine like terms: -2.702702703 + 2.702702703 = 0.000000000 0.000000000 + t = -2.895804376 + 2.702702703 t = -2.895804376 + 2.702702703 Combine like terms: -2.895804376 + 2.702702703 = -0.193101673 t = -0.193101673 Simplifying t = -0.193101673Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.598507079, -0.193101673}
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