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Simplifying 0 = -16t2 + 105t + -60 Reorder the terms: 0 = -60 + 105t + -16t2 Solving 0 = -60 + 105t + -16t2 Solving for variable 't'. Combine like terms: 0 + 60 = 60 60 + -105t + 16t2 = -60 + 105t + -16t2 + 60 + -105t + 16t2 Reorder the terms: 60 + -105t + 16t2 = -60 + 60 + 105t + -105t + -16t2 + 16t2 Combine like terms: -60 + 60 = 0 60 + -105t + 16t2 = 0 + 105t + -105t + -16t2 + 16t2 60 + -105t + 16t2 = 105t + -105t + -16t2 + 16t2 Combine like terms: 105t + -105t = 0 60 + -105t + 16t2 = 0 + -16t2 + 16t2 60 + -105t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 60 + -105t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.75 + -6.5625t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -6.5625t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -6.5625t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -6.5625t + t2 = 0 + -3.75 -6.5625t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -6.5625t + t2 = -3.75 The t term is -6.5625t. Take half its coefficient (-3.28125). Square it (10.76660156) and add it to both sides. Add '10.76660156' to each side of the equation. -6.5625t + 10.76660156 + t2 = -3.75 + 10.76660156 Reorder the terms: 10.76660156 + -6.5625t + t2 = -3.75 + 10.76660156 Combine like terms: -3.75 + 10.76660156 = 7.01660156 10.76660156 + -6.5625t + t2 = 7.01660156 Factor a perfect square on the left side: (t + -3.28125)(t + -3.28125) = 7.01660156 Calculate the square root of the right side: 2.648886853 Break this problem into two subproblems by setting (t + -3.28125) equal to 2.648886853 and -2.648886853.Subproblem 1
t + -3.28125 = 2.648886853 Simplifying t + -3.28125 = 2.648886853 Reorder the terms: -3.28125 + t = 2.648886853 Solving -3.28125 + t = 2.648886853 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + t = 2.648886853 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = 2.648886853 + 3.28125 t = 2.648886853 + 3.28125 Combine like terms: 2.648886853 + 3.28125 = 5.930136853 t = 5.930136853 Simplifying t = 5.930136853Subproblem 2
t + -3.28125 = -2.648886853 Simplifying t + -3.28125 = -2.648886853 Reorder the terms: -3.28125 + t = -2.648886853 Solving -3.28125 + t = -2.648886853 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + t = -2.648886853 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = -2.648886853 + 3.28125 t = -2.648886853 + 3.28125 Combine like terms: -2.648886853 + 3.28125 = 0.632363147 t = 0.632363147 Simplifying t = 0.632363147Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.930136853, 0.632363147}
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