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Simplifying 0 = 4.9t2 + 30t + 3.2 Reorder the terms: 0 = 3.2 + 30t + 4.9t2 Solving 0 = 3.2 + 30t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -3.2 = -3.2 -3.2 + -30t + -4.9t2 = 3.2 + 30t + 4.9t2 + -3.2 + -30t + -4.9t2 Reorder the terms: -3.2 + -30t + -4.9t2 = 3.2 + -3.2 + 30t + -30t + 4.9t2 + -4.9t2 Combine like terms: 3.2 + -3.2 = 0.0 -3.2 + -30t + -4.9t2 = 0.0 + 30t + -30t + 4.9t2 + -4.9t2 -3.2 + -30t + -4.9t2 = 30t + -30t + 4.9t2 + -4.9t2 Combine like terms: 30t + -30t = 0 -3.2 + -30t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -3.2 + -30t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -3.2 + -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'. 0.6530612245 + 6.12244898t + t2 = 0 Move the constant term to the right: Add '-0.6530612245' to each side of the equation. 0.6530612245 + 6.12244898t + -0.6530612245 + t2 = 0 + -0.6530612245 Reorder the terms: 0.6530612245 + -0.6530612245 + 6.12244898t + t2 = 0 + -0.6530612245 Combine like terms: 0.6530612245 + -0.6530612245 = 0.0000000000 0.0000000000 + 6.12244898t + t2 = 0 + -0.6530612245 6.12244898t + t2 = 0 + -0.6530612245 Combine like terms: 0 + -0.6530612245 = -0.6530612245 6.12244898t + t2 = -0.6530612245 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 = -0.6530612245 + 9.371095378 Reorder the terms: 9.371095378 + 6.12244898t + t2 = -0.6530612245 + 9.371095378 Combine like terms: -0.6530612245 + 9.371095378 = 8.7180341535 9.371095378 + 6.12244898t + t2 = 8.7180341535 Factor a perfect square on the left side: (t + 3.06122449)(t + 3.06122449) = 8.7180341535 Calculate the square root of the right side: 2.952631733 Break this problem into two subproblems by setting (t + 3.06122449) equal to 2.952631733 and -2.952631733.Subproblem 1
t + 3.06122449 = 2.952631733 Simplifying t + 3.06122449 = 2.952631733 Reorder the terms: 3.06122449 + t = 2.952631733 Solving 3.06122449 + t = 2.952631733 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 = 2.952631733 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = 2.952631733 + -3.06122449 t = 2.952631733 + -3.06122449 Combine like terms: 2.952631733 + -3.06122449 = -0.108592757 t = -0.108592757 Simplifying t = -0.108592757Subproblem 2
t + 3.06122449 = -2.952631733 Simplifying t + 3.06122449 = -2.952631733 Reorder the terms: 3.06122449 + t = -2.952631733 Solving 3.06122449 + t = -2.952631733 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 = -2.952631733 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = -2.952631733 + -3.06122449 t = -2.952631733 + -3.06122449 Combine like terms: -2.952631733 + -3.06122449 = -6.013856223 t = -6.013856223 Simplifying t = -6.013856223Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.108592757, -6.013856223}
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