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Simplifying 1 = -16t2 + 96t Reorder the terms: 1 = 96t + -16t2 Solving 1 = 96t + -16t2 Solving for variable 't'. Reorder the terms: 1 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 1 + -96t + 16t2 = 0 + -16t2 + 16t2 1 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1 + -96t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -6t + t2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -6t + -0.0625 + t2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -6t + t2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -6t + t2 = 0 + -0.0625 -6t + t2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -6t + t2 = -0.0625 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -0.0625 + 9 Reorder the terms: 9 + -6t + t2 = -0.0625 + 9 Combine like terms: -0.0625 + 9 = 8.9375 9 + -6t + t2 = 8.9375 Factor a perfect square on the left side: (t + -3)(t + -3) = 8.9375 Calculate the square root of the right side: 2.989565186 Break this problem into two subproblems by setting (t + -3) equal to 2.989565186 and -2.989565186.Subproblem 1
t + -3 = 2.989565186 Simplifying t + -3 = 2.989565186 Reorder the terms: -3 + t = 2.989565186 Solving -3 + t = 2.989565186 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.989565186 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.989565186 + 3 t = 2.989565186 + 3 Combine like terms: 2.989565186 + 3 = 5.989565186 t = 5.989565186 Simplifying t = 5.989565186Subproblem 2
t + -3 = -2.989565186 Simplifying t + -3 = -2.989565186 Reorder the terms: -3 + t = -2.989565186 Solving -3 + t = -2.989565186 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.989565186 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.989565186 + 3 t = -2.989565186 + 3 Combine like terms: -2.989565186 + 3 = 0.010434814 t = 0.010434814 Simplifying t = 0.010434814Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.989565186, 0.010434814}
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