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Simplifying 0 = -16t2 + 44t + 5 Reorder the terms: 0 = 5 + 44t + -16t2 Solving 0 = 5 + 44t + -16t2 Solving for variable 't'. Combine like terms: 0 + -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 = 2.203125 1.890625 + -2.75t + t2 = 2.203125 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = 2.203125 Calculate the square root of the right side: 1.484292761 Break this problem into two subproblems by setting (t + -1.375) equal to 1.484292761 and -1.484292761.Subproblem 1
t + -1.375 = 1.484292761 Simplifying t + -1.375 = 1.484292761 Reorder the terms: -1.375 + t = 1.484292761 Solving -1.375 + t = 1.484292761 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 = 1.484292761 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = 1.484292761 + 1.375 t = 1.484292761 + 1.375 Combine like terms: 1.484292761 + 1.375 = 2.859292761 t = 2.859292761 Simplifying t = 2.859292761Subproblem 2
t + -1.375 = -1.484292761 Simplifying t + -1.375 = -1.484292761 Reorder the terms: -1.375 + t = -1.484292761 Solving -1.375 + t = -1.484292761 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 = -1.484292761 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = -1.484292761 + 1.375 t = -1.484292761 + 1.375 Combine like terms: -1.484292761 + 1.375 = -0.109292761 t = -0.109292761 Simplifying t = -0.109292761Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.859292761, -0.109292761}
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