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Simplifying 35 = -4.9t2 + 30t Reorder the terms: 35 = 30t + -4.9t2 Solving 35 = 30t + -4.9t2 Solving for variable 't'. Reorder the terms: 35 + -30t + 4.9t2 = 30t + -30t + -4.9t2 + 4.9t2 Combine like terms: 30t + -30t = 0 35 + -30t + 4.9t2 = 0 + -4.9t2 + 4.9t2 35 + -30t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 35 + -30t + 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'. 7.142857143 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '-7.142857143' to each side of the equation. 7.142857143 + -6.12244898t + -7.142857143 + t2 = 0 + -7.142857143 Reorder the terms: 7.142857143 + -7.142857143 + -6.12244898t + t2 = 0 + -7.142857143 Combine like terms: 7.142857143 + -7.142857143 = 0.000000000 0.000000000 + -6.12244898t + t2 = 0 + -7.142857143 -6.12244898t + t2 = 0 + -7.142857143 Combine like terms: 0 + -7.142857143 = -7.142857143 -6.12244898t + t2 = -7.142857143 The t term is -6.12244898t. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898t + 9.371095378 + t2 = -7.142857143 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = -7.142857143 + 9.371095378 Combine like terms: -7.142857143 + 9.371095378 = 2.228238235 9.371095378 + -6.12244898t + t2 = 2.228238235 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 2.228238235 Calculate the square root of the right side: 1.492728453 Break this problem into two subproblems by setting (t + -3.06122449) equal to 1.492728453 and -1.492728453.Subproblem 1
t + -3.06122449 = 1.492728453 Simplifying t + -3.06122449 = 1.492728453 Reorder the terms: -3.06122449 + t = 1.492728453 Solving -3.06122449 + t = 1.492728453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = 1.492728453 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 1.492728453 + 3.06122449 t = 1.492728453 + 3.06122449 Combine like terms: 1.492728453 + 3.06122449 = 4.553952943 t = 4.553952943 Simplifying t = 4.553952943Subproblem 2
t + -3.06122449 = -1.492728453 Simplifying t + -3.06122449 = -1.492728453 Reorder the terms: -3.06122449 + t = -1.492728453 Solving -3.06122449 + t = -1.492728453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = -1.492728453 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -1.492728453 + 3.06122449 t = -1.492728453 + 3.06122449 Combine like terms: -1.492728453 + 3.06122449 = 1.568496037 t = 1.568496037 Simplifying t = 1.568496037Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.553952943, 1.568496037}
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