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Simplifying 0 = -16t2 + 75t + -87.890625 Reorder the terms: 0 = -87.890625 + 75t + -16t2 Solving 0 = -87.890625 + 75t + -16t2 Solving for variable 't'. Combine like terms: 0 + 87.890625 = 87.890625 87.890625 + -75t + 16t2 = -87.890625 + 75t + -16t2 + 87.890625 + -75t + 16t2 Reorder the terms: 87.890625 + -75t + 16t2 = -87.890625 + 87.890625 + 75t + -75t + -16t2 + 16t2 Combine like terms: -87.890625 + 87.890625 = 0.000000 87.890625 + -75t + 16t2 = 0.000000 + 75t + -75t + -16t2 + 16t2 87.890625 + -75t + 16t2 = 75t + -75t + -16t2 + 16t2 Combine like terms: 75t + -75t = 0 87.890625 + -75t + 16t2 = 0 + -16t2 + 16t2 87.890625 + -75t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 87.890625 + -75t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.493164063 + -4.6875t + t2 = 0 Move the constant term to the right: Add '-5.493164063' to each side of the equation. 5.493164063 + -4.6875t + -5.493164063 + t2 = 0 + -5.493164063 Reorder the terms: 5.493164063 + -5.493164063 + -4.6875t + t2 = 0 + -5.493164063 Combine like terms: 5.493164063 + -5.493164063 = 0.000000000 0.000000000 + -4.6875t + t2 = 0 + -5.493164063 -4.6875t + t2 = 0 + -5.493164063 Combine like terms: 0 + -5.493164063 = -5.493164063 -4.6875t + t2 = -5.493164063 The t term is -4.6875t. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875t + 5.493164063 + t2 = -5.493164063 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875t + t2 = -5.493164063 + 5.493164063 Combine like terms: -5.493164063 + 5.493164063 = 0.000000000 5.493164063 + -4.6875t + t2 = 0.000000000 Factor a perfect square on the left side: (t + -2.34375)(t + -2.34375) = 0.000000000 Calculate the square root of the right side: 0.000000000 Break this problem into two subproblems by setting (t + -2.34375) equal to 0.000000000 and 0.000000000.Subproblem 1
t + -2.34375 = 0.000000000 Simplifying t + -2.34375 = 0.000000000 Reorder the terms: -2.34375 + t = 0.000000000 Solving -2.34375 + t = 0.000000000 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = 0.000000000 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = 0.000000000 + 2.34375 t = 0.000000000 + 2.34375 Combine like terms: 0.000000000 + 2.34375 = 2.34375 t = 2.34375 Simplifying t = 2.34375Subproblem 2
t + -2.34375 = 0.000000000 Simplifying t + -2.34375 = 0.000000000 Reorder the terms: -2.34375 + t = 0.000000000 Solving -2.34375 + t = 0.000000000 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = 0.000000000 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = 0.000000000 + 2.34375 t = 0.000000000 + 2.34375 Combine like terms: 0.000000000 + 2.34375 = 2.34375 t = 2.34375 Simplifying t = 2.34375Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.34375, 2.34375}
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