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Simplifying 50 = -16t2 + 85t + 12 Reorder the terms: 50 = 12 + 85t + -16t2 Solving 50 = 12 + 85t + -16t2 Solving for variable 't'. Combine like terms: 50 + -12 = 38 38 + -85t + 16t2 = 12 + 85t + -16t2 + -12 + -85t + 16t2 Reorder the terms: 38 + -85t + 16t2 = 12 + -12 + 85t + -85t + -16t2 + 16t2 Combine like terms: 12 + -12 = 0 38 + -85t + 16t2 = 0 + 85t + -85t + -16t2 + 16t2 38 + -85t + 16t2 = 85t + -85t + -16t2 + 16t2 Combine like terms: 85t + -85t = 0 38 + -85t + 16t2 = 0 + -16t2 + 16t2 38 + -85t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 38 + -85t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.375 + -5.3125t + t2 = 0 Move the constant term to the right: Add '-2.375' to each side of the equation. 2.375 + -5.3125t + -2.375 + t2 = 0 + -2.375 Reorder the terms: 2.375 + -2.375 + -5.3125t + t2 = 0 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + -5.3125t + t2 = 0 + -2.375 -5.3125t + t2 = 0 + -2.375 Combine like terms: 0 + -2.375 = -2.375 -5.3125t + t2 = -2.375 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 = -2.375 + 7.055664063 Reorder the terms: 7.055664063 + -5.3125t + t2 = -2.375 + 7.055664063 Combine like terms: -2.375 + 7.055664063 = 4.680664063 7.055664063 + -5.3125t + t2 = 4.680664063 Factor a perfect square on the left side: (t + -2.65625)(t + -2.65625) = 4.680664063 Calculate the square root of the right side: 2.163484241 Break this problem into two subproblems by setting (t + -2.65625) equal to 2.163484241 and -2.163484241.Subproblem 1
t + -2.65625 = 2.163484241 Simplifying t + -2.65625 = 2.163484241 Reorder the terms: -2.65625 + t = 2.163484241 Solving -2.65625 + t = 2.163484241 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 = 2.163484241 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + t = 2.163484241 + 2.65625 t = 2.163484241 + 2.65625 Combine like terms: 2.163484241 + 2.65625 = 4.819734241 t = 4.819734241 Simplifying t = 4.819734241Subproblem 2
t + -2.65625 = -2.163484241 Simplifying t + -2.65625 = -2.163484241 Reorder the terms: -2.65625 + t = -2.163484241 Solving -2.65625 + t = -2.163484241 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 = -2.163484241 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + t = -2.163484241 + 2.65625 t = -2.163484241 + 2.65625 Combine like terms: -2.163484241 + 2.65625 = 0.492765759 t = 0.492765759 Simplifying t = 0.492765759Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.819734241, 0.492765759}
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