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Simplifying 8 = 50t + -9.8t2 Solving 8 = 50t + -9.8t2 Solving for variable 't'. Reorder the terms: 8 + -50t + 9.8t2 = 50t + -50t + -9.8t2 + 9.8t2 Combine like terms: 50t + -50t = 0 8 + -50t + 9.8t2 = 0 + -9.8t2 + 9.8t2 8 + -50t + 9.8t2 = -9.8t2 + 9.8t2 Combine like terms: -9.8t2 + 9.8t2 = 0.0 8 + -50t + 9.8t2 = 0.0 Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. 0.8163265306 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '-0.8163265306' to each side of the equation. 0.8163265306 + -5.102040816t + -0.8163265306 + t2 = 0 + -0.8163265306 Reorder the terms: 0.8163265306 + -0.8163265306 + -5.102040816t + t2 = 0 + -0.8163265306 Combine like terms: 0.8163265306 + -0.8163265306 = 0.0000000000 0.0000000000 + -5.102040816t + t2 = 0 + -0.8163265306 -5.102040816t + t2 = 0 + -0.8163265306 Combine like terms: 0 + -0.8163265306 = -0.8163265306 -5.102040816t + t2 = -0.8163265306 The t term is -5.102040816t. Take half its coefficient (-2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. -5.102040816t + 6.507705122 + t2 = -0.8163265306 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = -0.8163265306 + 6.507705122 Combine like terms: -0.8163265306 + 6.507705122 = 5.6913785914 6.507705122 + -5.102040816t + t2 = 5.6913785914 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 5.6913785914 Calculate the square root of the right side: 2.385661039 Break this problem into two subproblems by setting (t + -2.551020408) equal to 2.385661039 and -2.385661039.Subproblem 1
t + -2.551020408 = 2.385661039 Simplifying t + -2.551020408 = 2.385661039 Reorder the terms: -2.551020408 + t = 2.385661039 Solving -2.551020408 + t = 2.385661039 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = 2.385661039 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 2.385661039 + 2.551020408 t = 2.385661039 + 2.551020408 Combine like terms: 2.385661039 + 2.551020408 = 4.936681447 t = 4.936681447 Simplifying t = 4.936681447Subproblem 2
t + -2.551020408 = -2.385661039 Simplifying t + -2.551020408 = -2.385661039 Reorder the terms: -2.551020408 + t = -2.385661039 Solving -2.551020408 + t = -2.385661039 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = -2.385661039 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -2.385661039 + 2.551020408 t = -2.385661039 + 2.551020408 Combine like terms: -2.385661039 + 2.551020408 = 0.165359369 t = 0.165359369 Simplifying t = 0.165359369Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.936681447, 0.165359369}
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