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Simplifying 277 = -16t2 + 140t + 38 Reorder the terms: 277 = 38 + 140t + -16t2 Solving 277 = 38 + 140t + -16t2 Solving for variable 't'. Combine like terms: 277 + -38 = 239 239 + -140t + 16t2 = 38 + 140t + -16t2 + -38 + -140t + 16t2 Reorder the terms: 239 + -140t + 16t2 = 38 + -38 + 140t + -140t + -16t2 + 16t2 Combine like terms: 38 + -38 = 0 239 + -140t + 16t2 = 0 + 140t + -140t + -16t2 + 16t2 239 + -140t + 16t2 = 140t + -140t + -16t2 + 16t2 Combine like terms: 140t + -140t = 0 239 + -140t + 16t2 = 0 + -16t2 + 16t2 239 + -140t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 239 + -140t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 14.9375 + -8.75t + t2 = 0 Move the constant term to the right: Add '-14.9375' to each side of the equation. 14.9375 + -8.75t + -14.9375 + t2 = 0 + -14.9375 Reorder the terms: 14.9375 + -14.9375 + -8.75t + t2 = 0 + -14.9375 Combine like terms: 14.9375 + -14.9375 = 0.0000 0.0000 + -8.75t + t2 = 0 + -14.9375 -8.75t + t2 = 0 + -14.9375 Combine like terms: 0 + -14.9375 = -14.9375 -8.75t + t2 = -14.9375 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 = -14.9375 + 19.140625 Reorder the terms: 19.140625 + -8.75t + t2 = -14.9375 + 19.140625 Combine like terms: -14.9375 + 19.140625 = 4.203125 19.140625 + -8.75t + t2 = 4.203125 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 4.203125 Calculate the square root of the right side: 2.050152433 Break this problem into two subproblems by setting (t + -4.375) equal to 2.050152433 and -2.050152433.Subproblem 1
t + -4.375 = 2.050152433 Simplifying t + -4.375 = 2.050152433 Reorder the terms: -4.375 + t = 2.050152433 Solving -4.375 + t = 2.050152433 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 = 2.050152433 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 2.050152433 + 4.375 t = 2.050152433 + 4.375 Combine like terms: 2.050152433 + 4.375 = 6.425152433 t = 6.425152433 Simplifying t = 6.425152433Subproblem 2
t + -4.375 = -2.050152433 Simplifying t + -4.375 = -2.050152433 Reorder the terms: -4.375 + t = -2.050152433 Solving -4.375 + t = -2.050152433 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 = -2.050152433 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -2.050152433 + 4.375 t = -2.050152433 + 4.375 Combine like terms: -2.050152433 + 4.375 = 2.324847567 t = 2.324847567 Simplifying t = 2.324847567Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.425152433, 2.324847567}
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