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Simplifying 0 = -16t2 + 140t + 5 Reorder the terms: 0 = 5 + 140t + -16t2 Solving 0 = 5 + 140t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -140t + 16t2 = 5 + 140t + -16t2 + -5 + -140t + 16t2 Reorder the terms: -5 + -140t + 16t2 = 5 + -5 + 140t + -140t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + -140t + 16t2 = 0 + 140t + -140t + -16t2 + 16t2 -5 + -140t + 16t2 = 140t + -140t + -16t2 + 16t2 Combine like terms: 140t + -140t = 0 -5 + -140t + 16t2 = 0 + -16t2 + 16t2 -5 + -140t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -140t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -8.75t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -8.75t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -8.75t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -8.75t + t2 = 0 + 0.3125 -8.75t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -8.75t + t2 = 0.3125 The t term is -8.75t. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75t + 19.140625 + t2 = 0.3125 + 19.140625 Reorder the terms: 19.140625 + -8.75t + t2 = 0.3125 + 19.140625 Combine like terms: 0.3125 + 19.140625 = 19.453125 19.140625 + -8.75t + t2 = 19.453125 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 19.453125 Calculate the square root of the right side: 4.410569691 Break this problem into two subproblems by setting (t + -4.375) equal to 4.410569691 and -4.410569691.Subproblem 1
t + -4.375 = 4.410569691 Simplifying t + -4.375 = 4.410569691 Reorder the terms: -4.375 + t = 4.410569691 Solving -4.375 + t = 4.410569691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = 4.410569691 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 4.410569691 + 4.375 t = 4.410569691 + 4.375 Combine like terms: 4.410569691 + 4.375 = 8.785569691 t = 8.785569691 Simplifying t = 8.785569691Subproblem 2
t + -4.375 = -4.410569691 Simplifying t + -4.375 = -4.410569691 Reorder the terms: -4.375 + t = -4.410569691 Solving -4.375 + t = -4.410569691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = -4.410569691 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -4.410569691 + 4.375 t = -4.410569691 + 4.375 Combine like terms: -4.410569691 + 4.375 = -0.035569691 t = -0.035569691 Simplifying t = -0.035569691Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.785569691, -0.035569691}
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