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Simplifying 0 = -16t2 + 88t + 1353 Reorder the terms: 0 = 1353 + 88t + -16t2 Solving 0 = 1353 + 88t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1353 = -1353 -1353 + -88t + 16t2 = 1353 + 88t + -16t2 + -1353 + -88t + 16t2 Reorder the terms: -1353 + -88t + 16t2 = 1353 + -1353 + 88t + -88t + -16t2 + 16t2 Combine like terms: 1353 + -1353 = 0 -1353 + -88t + 16t2 = 0 + 88t + -88t + -16t2 + 16t2 -1353 + -88t + 16t2 = 88t + -88t + -16t2 + 16t2 Combine like terms: 88t + -88t = 0 -1353 + -88t + 16t2 = 0 + -16t2 + 16t2 -1353 + -88t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1353 + -88t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -84.5625 + -5.5t + t2 = 0 Move the constant term to the right: Add '84.5625' to each side of the equation. -84.5625 + -5.5t + 84.5625 + t2 = 0 + 84.5625 Reorder the terms: -84.5625 + 84.5625 + -5.5t + t2 = 0 + 84.5625 Combine like terms: -84.5625 + 84.5625 = 0.0000 0.0000 + -5.5t + t2 = 0 + 84.5625 -5.5t + t2 = 0 + 84.5625 Combine like terms: 0 + 84.5625 = 84.5625 -5.5t + t2 = 84.5625 The t term is -5.5t. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t + 7.5625 + t2 = 84.5625 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 84.5625 + 7.5625 Combine like terms: 84.5625 + 7.5625 = 92.125 7.5625 + -5.5t + t2 = 92.125 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 92.125 Calculate the square root of the right side: 9.59817691 Break this problem into two subproblems by setting (t + -2.75) equal to 9.59817691 and -9.59817691.Subproblem 1
t + -2.75 = 9.59817691 Simplifying t + -2.75 = 9.59817691 Reorder the terms: -2.75 + t = 9.59817691 Solving -2.75 + t = 9.59817691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = 9.59817691 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 9.59817691 + 2.75 t = 9.59817691 + 2.75 Combine like terms: 9.59817691 + 2.75 = 12.34817691 t = 12.34817691 Simplifying t = 12.34817691Subproblem 2
t + -2.75 = -9.59817691 Simplifying t + -2.75 = -9.59817691 Reorder the terms: -2.75 + t = -9.59817691 Solving -2.75 + t = -9.59817691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = -9.59817691 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -9.59817691 + 2.75 t = -9.59817691 + 2.75 Combine like terms: -9.59817691 + 2.75 = -6.84817691 t = -6.84817691 Simplifying t = -6.84817691Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.34817691, -6.84817691}
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