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Simplifying 73.446 = 0.112t2 + 0.340t Reorder the terms: 73.446 = 0.340t + 0.112t2 Solving 73.446 = 0.340t + 0.112t2 Solving for variable 't'. Reorder the terms: 73.446 + -0.340t + -0.112t2 = 0.340t + -0.340t + 0.112t2 + -0.112t2 Combine like terms: 0.340t + -0.340t = 0.000 73.446 + -0.340t + -0.112t2 = 0.000 + 0.112t2 + -0.112t2 73.446 + -0.340t + -0.112t2 = 0.112t2 + -0.112t2 Combine like terms: 0.112t2 + -0.112t2 = 0.000 73.446 + -0.340t + -0.112t2 = 0.000 Begin completing the square. Divide all terms by -0.112 the coefficient of the squared term: Divide each side by '-0.112'. -655.7678571 + 3.035714286t + t2 = 0 Move the constant term to the right: Add '655.7678571' to each side of the equation. -655.7678571 + 3.035714286t + 655.7678571 + t2 = 0 + 655.7678571 Reorder the terms: -655.7678571 + 655.7678571 + 3.035714286t + t2 = 0 + 655.7678571 Combine like terms: -655.7678571 + 655.7678571 = 0.0000000 0.0000000 + 3.035714286t + t2 = 0 + 655.7678571 3.035714286t + t2 = 0 + 655.7678571 Combine like terms: 0 + 655.7678571 = 655.7678571 3.035714286t + t2 = 655.7678571 The t term is 3.035714286t. Take half its coefficient (1.517857143). Square it (2.303890307) and add it to both sides. Add '2.303890307' to each side of the equation. 3.035714286t + 2.303890307 + t2 = 655.7678571 + 2.303890307 Reorder the terms: 2.303890307 + 3.035714286t + t2 = 655.7678571 + 2.303890307 Combine like terms: 655.7678571 + 2.303890307 = 658.071747407 2.303890307 + 3.035714286t + t2 = 658.071747407 Factor a perfect square on the left side: (t + 1.517857143)(t + 1.517857143) = 658.071747407 Calculate the square root of the right side: 25.652909141 Break this problem into two subproblems by setting (t + 1.517857143) equal to 25.652909141 and -25.652909141.Subproblem 1
t + 1.517857143 = 25.652909141 Simplifying t + 1.517857143 = 25.652909141 Reorder the terms: 1.517857143 + t = 25.652909141 Solving 1.517857143 + t = 25.652909141 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.517857143' to each side of the equation. 1.517857143 + -1.517857143 + t = 25.652909141 + -1.517857143 Combine like terms: 1.517857143 + -1.517857143 = 0.000000000 0.000000000 + t = 25.652909141 + -1.517857143 t = 25.652909141 + -1.517857143 Combine like terms: 25.652909141 + -1.517857143 = 24.135051998 t = 24.135051998 Simplifying t = 24.135051998Subproblem 2
t + 1.517857143 = -25.652909141 Simplifying t + 1.517857143 = -25.652909141 Reorder the terms: 1.517857143 + t = -25.652909141 Solving 1.517857143 + t = -25.652909141 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.517857143' to each side of the equation. 1.517857143 + -1.517857143 + t = -25.652909141 + -1.517857143 Combine like terms: 1.517857143 + -1.517857143 = 0.000000000 0.000000000 + t = -25.652909141 + -1.517857143 t = -25.652909141 + -1.517857143 Combine like terms: -25.652909141 + -1.517857143 = -27.170766284 t = -27.170766284 Simplifying t = -27.170766284Solution
The solution to the problem is based on the solutions from the subproblems. t = {24.135051998, -27.170766284}
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