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Simplifying 34.44 = -16t2 + 44t + 5 Reorder the terms: 34.44 = 5 + 44t + -16t2 Solving 34.44 = 5 + 44t + -16t2 Solving for variable 't'. Combine like terms: 34.44 + -5 = 29.44 29.44 + -44t + 16t2 = 5 + 44t + -16t2 + -5 + -44t + 16t2 Reorder the terms: 29.44 + -44t + 16t2 = 5 + -5 + 44t + -44t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 29.44 + -44t + 16t2 = 0 + 44t + -44t + -16t2 + 16t2 29.44 + -44t + 16t2 = 44t + -44t + -16t2 + 16t2 Combine like terms: 44t + -44t = 0 29.44 + -44t + 16t2 = 0 + -16t2 + 16t2 29.44 + -44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 29.44 + -44t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.84 + -2.75t + t2 = 0 Move the constant term to the right: Add '-1.84' to each side of the equation. 1.84 + -2.75t + -1.84 + t2 = 0 + -1.84 Reorder the terms: 1.84 + -1.84 + -2.75t + t2 = 0 + -1.84 Combine like terms: 1.84 + -1.84 = 0.00 0.00 + -2.75t + t2 = 0 + -1.84 -2.75t + t2 = 0 + -1.84 Combine like terms: 0 + -1.84 = -1.84 -2.75t + t2 = -1.84 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 = -1.84 + 1.890625 Reorder the terms: 1.890625 + -2.75t + t2 = -1.84 + 1.890625 Combine like terms: -1.84 + 1.890625 = 0.050625 1.890625 + -2.75t + t2 = 0.050625 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = 0.050625 Calculate the square root of the right side: 0.225 Break this problem into two subproblems by setting (t + -1.375) equal to 0.225 and -0.225.Subproblem 1
t + -1.375 = 0.225 Simplifying t + -1.375 = 0.225 Reorder the terms: -1.375 + t = 0.225 Solving -1.375 + t = 0.225 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 = 0.225 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = 0.225 + 1.375 t = 0.225 + 1.375 Combine like terms: 0.225 + 1.375 = 1.6 t = 1.6 Simplifying t = 1.6Subproblem 2
t + -1.375 = -0.225 Simplifying t + -1.375 = -0.225 Reorder the terms: -1.375 + t = -0.225 Solving -1.375 + t = -0.225 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 = -0.225 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = -0.225 + 1.375 t = -0.225 + 1.375 Combine like terms: -0.225 + 1.375 = 1.15 t = 1.15 Simplifying t = 1.15Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.6, 1.15}
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