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Simplifying 16.115t2 + 160t + -397.14 = 0 Reorder the terms: -397.14 + 160t + 16.115t2 = 0 Solving -397.14 + 160t + 16.115t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16.115 the coefficient of the squared term: Divide each side by '16.115'. -24.64412038 + 9.928637915t + t2 = 0 Move the constant term to the right: Add '24.64412038' to each side of the equation. -24.64412038 + 9.928637915t + 24.64412038 + t2 = 0 + 24.64412038 Reorder the terms: -24.64412038 + 24.64412038 + 9.928637915t + t2 = 0 + 24.64412038 Combine like terms: -24.64412038 + 24.64412038 = 0.00000000 0.00000000 + 9.928637915t + t2 = 0 + 24.64412038 9.928637915t + t2 = 0 + 24.64412038 Combine like terms: 0 + 24.64412038 = 24.64412038 9.928637915t + t2 = 24.64412038 The t term is 9.928637915t. Take half its coefficient (4.964318958). Square it (24.64446272) and add it to both sides. Add '24.64446272' to each side of the equation. 9.928637915t + 24.64446272 + t2 = 24.64412038 + 24.64446272 Reorder the terms: 24.64446272 + 9.928637915t + t2 = 24.64412038 + 24.64446272 Combine like terms: 24.64412038 + 24.64446272 = 49.2885831 24.64446272 + 9.928637915t + t2 = 49.2885831 Factor a perfect square on the left side: (t + 4.964318958)(t + 4.964318958) = 49.2885831 Calculate the square root of the right side: 7.020582818 Break this problem into two subproblems by setting (t + 4.964318958) equal to 7.020582818 and -7.020582818.Subproblem 1
t + 4.964318958 = 7.020582818 Simplifying t + 4.964318958 = 7.020582818 Reorder the terms: 4.964318958 + t = 7.020582818 Solving 4.964318958 + t = 7.020582818 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.964318958' to each side of the equation. 4.964318958 + -4.964318958 + t = 7.020582818 + -4.964318958 Combine like terms: 4.964318958 + -4.964318958 = 0.000000000 0.000000000 + t = 7.020582818 + -4.964318958 t = 7.020582818 + -4.964318958 Combine like terms: 7.020582818 + -4.964318958 = 2.05626386 t = 2.05626386 Simplifying t = 2.05626386Subproblem 2
t + 4.964318958 = -7.020582818 Simplifying t + 4.964318958 = -7.020582818 Reorder the terms: 4.964318958 + t = -7.020582818 Solving 4.964318958 + t = -7.020582818 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.964318958' to each side of the equation. 4.964318958 + -4.964318958 + t = -7.020582818 + -4.964318958 Combine like terms: 4.964318958 + -4.964318958 = 0.000000000 0.000000000 + t = -7.020582818 + -4.964318958 t = -7.020582818 + -4.964318958 Combine like terms: -7.020582818 + -4.964318958 = -11.984901776 t = -11.984901776 Simplifying t = -11.984901776Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.05626386, -11.984901776}
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