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Simplifying 35 = -4.9t2 + 30t + 1.6 Reorder the terms: 35 = 1.6 + 30t + -4.9t2 Solving 35 = 1.6 + 30t + -4.9t2 Solving for variable 't'. Combine like terms: 35 + -1.6 = 33.4 33.4 + -30t + 4.9t2 = 1.6 + 30t + -4.9t2 + -1.6 + -30t + 4.9t2 Reorder the terms: 33.4 + -30t + 4.9t2 = 1.6 + -1.6 + 30t + -30t + -4.9t2 + 4.9t2 Combine like terms: 1.6 + -1.6 = 0.0 33.4 + -30t + 4.9t2 = 0.0 + 30t + -30t + -4.9t2 + 4.9t2 33.4 + -30t + 4.9t2 = 30t + -30t + -4.9t2 + 4.9t2 Combine like terms: 30t + -30t = 0 33.4 + -30t + 4.9t2 = 0 + -4.9t2 + 4.9t2 33.4 + -30t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 33.4 + -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'. 6.816326531 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '-6.816326531' to each side of the equation. 6.816326531 + -6.12244898t + -6.816326531 + t2 = 0 + -6.816326531 Reorder the terms: 6.816326531 + -6.816326531 + -6.12244898t + t2 = 0 + -6.816326531 Combine like terms: 6.816326531 + -6.816326531 = 0.000000000 0.000000000 + -6.12244898t + t2 = 0 + -6.816326531 -6.12244898t + t2 = 0 + -6.816326531 Combine like terms: 0 + -6.816326531 = -6.816326531 -6.12244898t + t2 = -6.816326531 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 = -6.816326531 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = -6.816326531 + 9.371095378 Combine like terms: -6.816326531 + 9.371095378 = 2.554768847 9.371095378 + -6.12244898t + t2 = 2.554768847 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 2.554768847 Calculate the square root of the right side: 1.598364429 Break this problem into two subproblems by setting (t + -3.06122449) equal to 1.598364429 and -1.598364429.Subproblem 1
t + -3.06122449 = 1.598364429 Simplifying t + -3.06122449 = 1.598364429 Reorder the terms: -3.06122449 + t = 1.598364429 Solving -3.06122449 + t = 1.598364429 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 = 1.598364429 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 1.598364429 + 3.06122449 t = 1.598364429 + 3.06122449 Combine like terms: 1.598364429 + 3.06122449 = 4.659588919 t = 4.659588919 Simplifying t = 4.659588919Subproblem 2
t + -3.06122449 = -1.598364429 Simplifying t + -3.06122449 = -1.598364429 Reorder the terms: -3.06122449 + t = -1.598364429 Solving -3.06122449 + t = -1.598364429 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 = -1.598364429 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -1.598364429 + 3.06122449 t = -1.598364429 + 3.06122449 Combine like terms: -1.598364429 + 3.06122449 = 1.462860061 t = 1.462860061 Simplifying t = 1.462860061Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.659588919, 1.462860061}
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