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Simplifying 14 = 1.65 + -0.0056t + 0.001683t2 Solving 14 = 1.65 + -0.0056t + 0.001683t2 Solving for variable 't'. Combine like terms: 14 + -1.65 = 12.35 12.35 + 0.0056t + -0.001683t2 = 1.65 + -0.0056t + 0.001683t2 + -1.65 + 0.0056t + -0.001683t2 Reorder the terms: 12.35 + 0.0056t + -0.001683t2 = 1.65 + -1.65 + -0.0056t + 0.0056t + 0.001683t2 + -0.001683t2 Combine like terms: 1.65 + -1.65 = 0.00 12.35 + 0.0056t + -0.001683t2 = 0.00 + -0.0056t + 0.0056t + 0.001683t2 + -0.001683t2 12.35 + 0.0056t + -0.001683t2 = -0.0056t + 0.0056t + 0.001683t2 + -0.001683t2 Combine like terms: -0.0056t + 0.0056t = 0.0000 12.35 + 0.0056t + -0.001683t2 = 0.0000 + 0.001683t2 + -0.001683t2 12.35 + 0.0056t + -0.001683t2 = 0.001683t2 + -0.001683t2 Combine like terms: 0.001683t2 + -0.001683t2 = 0.000000 12.35 + 0.0056t + -0.001683t2 = 0.000000 Begin completing the square. Divide all terms by -0.001683 the coefficient of the squared term: Divide each side by '-0.001683'. -7338.08675 + -3.327391563t + t2 = 0 Move the constant term to the right: Add '7338.08675' to each side of the equation. -7338.08675 + -3.327391563t + 7338.08675 + t2 = 0 + 7338.08675 Reorder the terms: -7338.08675 + 7338.08675 + -3.327391563t + t2 = 0 + 7338.08675 Combine like terms: -7338.08675 + 7338.08675 = 0.00000 0.00000 + -3.327391563t + t2 = 0 + 7338.08675 -3.327391563t + t2 = 0 + 7338.08675 Combine like terms: 0 + 7338.08675 = 7338.08675 -3.327391563t + t2 = 7338.08675 The t term is -3.327391563t. Take half its coefficient (-1.663695782). Square it (2.767883655) and add it to both sides. Add '2.767883655' to each side of the equation. -3.327391563t + 2.767883655 + t2 = 7338.08675 + 2.767883655 Reorder the terms: 2.767883655 + -3.327391563t + t2 = 7338.08675 + 2.767883655 Combine like terms: 7338.08675 + 2.767883655 = 7340.854633655 2.767883655 + -3.327391563t + t2 = 7340.854633655 Factor a perfect square on the left side: (t + -1.663695782)(t + -1.663695782) = 7340.854633655 Calculate the square root of the right side: 85.678787536 Break this problem into two subproblems by setting (t + -1.663695782) equal to 85.678787536 and -85.678787536.Subproblem 1
t + -1.663695782 = 85.678787536 Simplifying t + -1.663695782 = 85.678787536 Reorder the terms: -1.663695782 + t = 85.678787536 Solving -1.663695782 + t = 85.678787536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.663695782' to each side of the equation. -1.663695782 + 1.663695782 + t = 85.678787536 + 1.663695782 Combine like terms: -1.663695782 + 1.663695782 = 0.000000000 0.000000000 + t = 85.678787536 + 1.663695782 t = 85.678787536 + 1.663695782 Combine like terms: 85.678787536 + 1.663695782 = 87.342483318 t = 87.342483318 Simplifying t = 87.342483318Subproblem 2
t + -1.663695782 = -85.678787536 Simplifying t + -1.663695782 = -85.678787536 Reorder the terms: -1.663695782 + t = -85.678787536 Solving -1.663695782 + t = -85.678787536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.663695782' to each side of the equation. -1.663695782 + 1.663695782 + t = -85.678787536 + 1.663695782 Combine like terms: -1.663695782 + 1.663695782 = 0.000000000 0.000000000 + t = -85.678787536 + 1.663695782 t = -85.678787536 + 1.663695782 Combine like terms: -85.678787536 + 1.663695782 = -84.015091754 t = -84.015091754 Simplifying t = -84.015091754Solution
The solution to the problem is based on the solutions from the subproblems. t = {87.342483318, -84.015091754}
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