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Simplifying 50 = -16t2 + 85t Reorder the terms: 50 = 85t + -16t2 Solving 50 = 85t + -16t2 Solving for variable 't'. Reorder the terms: 50 + -85t + 16t2 = 85t + -85t + -16t2 + 16t2 Combine like terms: 85t + -85t = 0 50 + -85t + 16t2 = 0 + -16t2 + 16t2 50 + -85t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 50 + -85t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.125 + -5.3125t + t2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -5.3125t + -3.125 + t2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -5.3125t + t2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -5.3125t + t2 = 0 + -3.125 -5.3125t + t2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -5.3125t + t2 = -3.125 The t term is -5.3125t. Take half its coefficient (-2.65625). Square it (7.055664063) and add it to both sides. Add '7.055664063' to each side of the equation. -5.3125t + 7.055664063 + t2 = -3.125 + 7.055664063 Reorder the terms: 7.055664063 + -5.3125t + t2 = -3.125 + 7.055664063 Combine like terms: -3.125 + 7.055664063 = 3.930664063 7.055664063 + -5.3125t + t2 = 3.930664063 Factor a perfect square on the left side: (t + -2.65625)(t + -2.65625) = 3.930664063 Calculate the square root of the right side: 1.982590241 Break this problem into two subproblems by setting (t + -2.65625) equal to 1.982590241 and -1.982590241.Subproblem 1
t + -2.65625 = 1.982590241 Simplifying t + -2.65625 = 1.982590241 Reorder the terms: -2.65625 + t = 1.982590241 Solving -2.65625 + t = 1.982590241 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.65625' to each side of the equation. -2.65625 + 2.65625 + t = 1.982590241 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + t = 1.982590241 + 2.65625 t = 1.982590241 + 2.65625 Combine like terms: 1.982590241 + 2.65625 = 4.638840241 t = 4.638840241 Simplifying t = 4.638840241Subproblem 2
t + -2.65625 = -1.982590241 Simplifying t + -2.65625 = -1.982590241 Reorder the terms: -2.65625 + t = -1.982590241 Solving -2.65625 + t = -1.982590241 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.65625' to each side of the equation. -2.65625 + 2.65625 + t = -1.982590241 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + t = -1.982590241 + 2.65625 t = -1.982590241 + 2.65625 Combine like terms: -1.982590241 + 2.65625 = 0.673659759 t = 0.673659759 Simplifying t = 0.673659759Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.638840241, 0.673659759}
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