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Simplifying -16t2 + 88t + 104 = 1 Reorder the terms: 104 + 88t + -16t2 = 1 Solving 104 + 88t + -16t2 = 1 Solving for variable 't'. Reorder the terms: 104 + -1 + 88t + -16t2 = 1 + -1 Combine like terms: 104 + -1 = 103 103 + 88t + -16t2 = 1 + -1 Combine like terms: 1 + -1 = 0 103 + 88t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -6.4375 + -5.5t + t2 = 0 Move the constant term to the right: Add '6.4375' to each side of the equation. -6.4375 + -5.5t + 6.4375 + t2 = 0 + 6.4375 Reorder the terms: -6.4375 + 6.4375 + -5.5t + t2 = 0 + 6.4375 Combine like terms: -6.4375 + 6.4375 = 0.0000 0.0000 + -5.5t + t2 = 0 + 6.4375 -5.5t + t2 = 0 + 6.4375 Combine like terms: 0 + 6.4375 = 6.4375 -5.5t + t2 = 6.4375 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 = 6.4375 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 6.4375 + 7.5625 Combine like terms: 6.4375 + 7.5625 = 14 7.5625 + -5.5t + t2 = 14 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (t + -2.75) equal to 3.741657387 and -3.741657387.Subproblem 1
t + -2.75 = 3.741657387 Simplifying t + -2.75 = 3.741657387 Reorder the terms: -2.75 + t = 3.741657387 Solving -2.75 + t = 3.741657387 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 = 3.741657387 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 3.741657387 + 2.75 t = 3.741657387 + 2.75 Combine like terms: 3.741657387 + 2.75 = 6.491657387 t = 6.491657387 Simplifying t = 6.491657387Subproblem 2
t + -2.75 = -3.741657387 Simplifying t + -2.75 = -3.741657387 Reorder the terms: -2.75 + t = -3.741657387 Solving -2.75 + t = -3.741657387 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 = -3.741657387 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -3.741657387 + 2.75 t = -3.741657387 + 2.75 Combine like terms: -3.741657387 + 2.75 = -0.991657387 t = -0.991657387 Simplifying t = -0.991657387Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.491657387, -0.991657387}
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