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Simplifying 10 = -16t2 + -44t + 5 Reorder the terms: 10 = 5 + -44t + -16t2 Solving 10 = 5 + -44t + -16t2 Solving for variable 't'. Combine like terms: 10 + -5 = 5 5 + 44t + 16t2 = 5 + -44t + -16t2 + -5 + 44t + 16t2 Reorder the terms: 5 + 44t + 16t2 = 5 + -5 + -44t + 44t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 5 + 44t + 16t2 = 0 + -44t + 44t + -16t2 + 16t2 5 + 44t + 16t2 = -44t + 44t + -16t2 + 16t2 Combine like terms: -44t + 44t = 0 5 + 44t + 16t2 = 0 + -16t2 + 16t2 5 + 44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 5 + 44t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + 2.75t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + 2.75t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + 2.75t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + 2.75t + t2 = 0 + -0.3125 2.75t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 2.75t + t2 = -0.3125 The t term is 2.75t. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75t + 1.890625 + t2 = -0.3125 + 1.890625 Reorder the terms: 1.890625 + 2.75t + t2 = -0.3125 + 1.890625 Combine like terms: -0.3125 + 1.890625 = 1.578125 1.890625 + 2.75t + t2 = 1.578125 Factor a perfect square on the left side: (t + 1.375)(t + 1.375) = 1.578125 Calculate the square root of the right side: 1.256234453 Break this problem into two subproblems by setting (t + 1.375) equal to 1.256234453 and -1.256234453.Subproblem 1
t + 1.375 = 1.256234453 Simplifying t + 1.375 = 1.256234453 Reorder the terms: 1.375 + t = 1.256234453 Solving 1.375 + t = 1.256234453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = 1.256234453 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = 1.256234453 + -1.375 t = 1.256234453 + -1.375 Combine like terms: 1.256234453 + -1.375 = -0.118765547 t = -0.118765547 Simplifying t = -0.118765547Subproblem 2
t + 1.375 = -1.256234453 Simplifying t + 1.375 = -1.256234453 Reorder the terms: 1.375 + t = -1.256234453 Solving 1.375 + t = -1.256234453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = -1.256234453 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = -1.256234453 + -1.375 t = -1.256234453 + -1.375 Combine like terms: -1.256234453 + -1.375 = -2.631234453 t = -2.631234453 Simplifying t = -2.631234453Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.118765547, -2.631234453}
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