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Simplifying 0 = -16t2 + -50t + 7 Reorder the terms: 0 = 7 + -50t + -16t2 Solving 0 = 7 + -50t + -16t2 Solving for variable 't'. Combine like terms: 0 + -7 = -7 -7 + 50t + 16t2 = 7 + -50t + -16t2 + -7 + 50t + 16t2 Reorder the terms: -7 + 50t + 16t2 = 7 + -7 + -50t + 50t + -16t2 + 16t2 Combine like terms: 7 + -7 = 0 -7 + 50t + 16t2 = 0 + -50t + 50t + -16t2 + 16t2 -7 + 50t + 16t2 = -50t + 50t + -16t2 + 16t2 Combine like terms: -50t + 50t = 0 -7 + 50t + 16t2 = 0 + -16t2 + 16t2 -7 + 50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -7 + 50t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + 3.125t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + 3.125t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + 3.125t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + 3.125t + t2 = 0 + 0.4375 3.125t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 3.125t + t2 = 0.4375 The t term is 3.125t. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125t + 2.44140625 + t2 = 0.4375 + 2.44140625 Reorder the terms: 2.44140625 + 3.125t + t2 = 0.4375 + 2.44140625 Combine like terms: 0.4375 + 2.44140625 = 2.87890625 2.44140625 + 3.125t + t2 = 2.87890625 Factor a perfect square on the left side: (t + 1.5625)(t + 1.5625) = 2.87890625 Calculate the square root of the right side: 1.696733995 Break this problem into two subproblems by setting (t + 1.5625) equal to 1.696733995 and -1.696733995.Subproblem 1
t + 1.5625 = 1.696733995 Simplifying t + 1.5625 = 1.696733995 Reorder the terms: 1.5625 + t = 1.696733995 Solving 1.5625 + t = 1.696733995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + t = 1.696733995 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = 1.696733995 + -1.5625 t = 1.696733995 + -1.5625 Combine like terms: 1.696733995 + -1.5625 = 0.134233995 t = 0.134233995 Simplifying t = 0.134233995Subproblem 2
t + 1.5625 = -1.696733995 Simplifying t + 1.5625 = -1.696733995 Reorder the terms: 1.5625 + t = -1.696733995 Solving 1.5625 + t = -1.696733995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + t = -1.696733995 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = -1.696733995 + -1.5625 t = -1.696733995 + -1.5625 Combine like terms: -1.696733995 + -1.5625 = -3.259233995 t = -3.259233995 Simplifying t = -3.259233995Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.134233995, -3.259233995}
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