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Simplifying t = -16t2 + 160t + 50 Reorder the terms: t = 50 + 160t + -16t2 Solving t = 50 + 160t + -16t2 Solving for variable 't'. Reorder the terms: -50 + t + -160t + 16t2 = 50 + 160t + -16t2 + -50 + -160t + 16t2 Combine like terms: t + -160t = -159t -50 + -159t + 16t2 = 50 + 160t + -16t2 + -50 + -160t + 16t2 Reorder the terms: -50 + -159t + 16t2 = 50 + -50 + 160t + -160t + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -50 + -159t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2 -50 + -159t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 -50 + -159t + 16t2 = 0 + -16t2 + 16t2 -50 + -159t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -50 + -159t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.125 + -9.9375t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -9.9375t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -9.9375t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -9.9375t + t2 = 0 + 3.125 -9.9375t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -9.9375t + t2 = 3.125 The t term is -9.9375t. Take half its coefficient (-4.96875). Square it (24.68847656) and add it to both sides. Add '24.68847656' to each side of the equation. -9.9375t + 24.68847656 + t2 = 3.125 + 24.68847656 Reorder the terms: 24.68847656 + -9.9375t + t2 = 3.125 + 24.68847656 Combine like terms: 3.125 + 24.68847656 = 27.81347656 24.68847656 + -9.9375t + t2 = 27.81347656 Factor a perfect square on the left side: (t + -4.96875)(t + -4.96875) = 27.81347656 Calculate the square root of the right side: 5.273848363 Break this problem into two subproblems by setting (t + -4.96875) equal to 5.273848363 and -5.273848363.Subproblem 1
t + -4.96875 = 5.273848363 Simplifying t + -4.96875 = 5.273848363 Reorder the terms: -4.96875 + t = 5.273848363 Solving -4.96875 + t = 5.273848363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.96875' to each side of the equation. -4.96875 + 4.96875 + t = 5.273848363 + 4.96875 Combine like terms: -4.96875 + 4.96875 = 0.00000 0.00000 + t = 5.273848363 + 4.96875 t = 5.273848363 + 4.96875 Combine like terms: 5.273848363 + 4.96875 = 10.242598363 t = 10.242598363 Simplifying t = 10.242598363Subproblem 2
t + -4.96875 = -5.273848363 Simplifying t + -4.96875 = -5.273848363 Reorder the terms: -4.96875 + t = -5.273848363 Solving -4.96875 + t = -5.273848363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.96875' to each side of the equation. -4.96875 + 4.96875 + t = -5.273848363 + 4.96875 Combine like terms: -4.96875 + 4.96875 = 0.00000 0.00000 + t = -5.273848363 + 4.96875 t = -5.273848363 + 4.96875 Combine like terms: -5.273848363 + 4.96875 = -0.305098363 t = -0.305098363 Simplifying t = -0.305098363Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.242598363, -0.305098363}
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