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Simplifying 55(t) = -16t2 + 64 + 55 Reorder the terms: 55t = 64 + 55 + -16t2 Combine like terms: 64 + 55 = 119 55t = 119 + -16t2 Solving 55t = 119 + -16t2 Solving for variable 't'. Reorder the terms: -119 + 55t + 16t2 = 119 + -16t2 + -119 + 16t2 Reorder the terms: -119 + 55t + 16t2 = 119 + -119 + -16t2 + 16t2 Combine like terms: 119 + -119 = 0 -119 + 55t + 16t2 = 0 + -16t2 + 16t2 -119 + 55t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -119 + 55t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7.4375 + 3.4375t + t2 = 0 Move the constant term to the right: Add '7.4375' to each side of the equation. -7.4375 + 3.4375t + 7.4375 + t2 = 0 + 7.4375 Reorder the terms: -7.4375 + 7.4375 + 3.4375t + t2 = 0 + 7.4375 Combine like terms: -7.4375 + 7.4375 = 0.0000 0.0000 + 3.4375t + t2 = 0 + 7.4375 3.4375t + t2 = 0 + 7.4375 Combine like terms: 0 + 7.4375 = 7.4375 3.4375t + t2 = 7.4375 The t term is 3.4375t. Take half its coefficient (1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. 3.4375t + 2.954101563 + t2 = 7.4375 + 2.954101563 Reorder the terms: 2.954101563 + 3.4375t + t2 = 7.4375 + 2.954101563 Combine like terms: 7.4375 + 2.954101563 = 10.391601563 2.954101563 + 3.4375t + t2 = 10.391601563 Factor a perfect square on the left side: (t + 1.71875)(t + 1.71875) = 10.391601563 Calculate the square root of the right side: 3.223600714 Break this problem into two subproblems by setting (t + 1.71875) equal to 3.223600714 and -3.223600714.Subproblem 1
t + 1.71875 = 3.223600714 Simplifying t + 1.71875 = 3.223600714 Reorder the terms: 1.71875 + t = 3.223600714 Solving 1.71875 + t = 3.223600714 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.71875' to each side of the equation. 1.71875 + -1.71875 + t = 3.223600714 + -1.71875 Combine like terms: 1.71875 + -1.71875 = 0.00000 0.00000 + t = 3.223600714 + -1.71875 t = 3.223600714 + -1.71875 Combine like terms: 3.223600714 + -1.71875 = 1.504850714 t = 1.504850714 Simplifying t = 1.504850714Subproblem 2
t + 1.71875 = -3.223600714 Simplifying t + 1.71875 = -3.223600714 Reorder the terms: 1.71875 + t = -3.223600714 Solving 1.71875 + t = -3.223600714 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.71875' to each side of the equation. 1.71875 + -1.71875 + t = -3.223600714 + -1.71875 Combine like terms: 1.71875 + -1.71875 = 0.00000 0.00000 + t = -3.223600714 + -1.71875 t = -3.223600714 + -1.71875 Combine like terms: -3.223600714 + -1.71875 = -4.942350714 t = -4.942350714 Simplifying t = -4.942350714Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.504850714, -4.942350714}
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