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Simplifying 0 = -16t2 + 18t + 25 Reorder the terms: 0 = 25 + 18t + -16t2 Solving 0 = 25 + 18t + -16t2 Solving for variable 't'. Combine like terms: 0 + -25 = -25 -25 + -18t + 16t2 = 25 + 18t + -16t2 + -25 + -18t + 16t2 Reorder the terms: -25 + -18t + 16t2 = 25 + -25 + 18t + -18t + -16t2 + 16t2 Combine like terms: 25 + -25 = 0 -25 + -18t + 16t2 = 0 + 18t + -18t + -16t2 + 16t2 -25 + -18t + 16t2 = 18t + -18t + -16t2 + 16t2 Combine like terms: 18t + -18t = 0 -25 + -18t + 16t2 = 0 + -16t2 + 16t2 -25 + -18t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -25 + -18t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + -1.125t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -1.125t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -1.125t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -1.125t + t2 = 0 + 1.5625 -1.125t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -1.125t + t2 = 1.5625 The t term is -1.125t. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125t + 0.31640625 + t2 = 1.5625 + 0.31640625 Reorder the terms: 0.31640625 + -1.125t + t2 = 1.5625 + 0.31640625 Combine like terms: 1.5625 + 0.31640625 = 1.87890625 0.31640625 + -1.125t + t2 = 1.87890625 Factor a perfect square on the left side: (t + -0.5625)(t + -0.5625) = 1.87890625 Calculate the square root of the right side: 1.370732012 Break this problem into two subproblems by setting (t + -0.5625) equal to 1.370732012 and -1.370732012.Subproblem 1
t + -0.5625 = 1.370732012 Simplifying t + -0.5625 = 1.370732012 Reorder the terms: -0.5625 + t = 1.370732012 Solving -0.5625 + t = 1.370732012 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + t = 1.370732012 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t = 1.370732012 + 0.5625 t = 1.370732012 + 0.5625 Combine like terms: 1.370732012 + 0.5625 = 1.933232012 t = 1.933232012 Simplifying t = 1.933232012Subproblem 2
t + -0.5625 = -1.370732012 Simplifying t + -0.5625 = -1.370732012 Reorder the terms: -0.5625 + t = -1.370732012 Solving -0.5625 + t = -1.370732012 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + t = -1.370732012 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t = -1.370732012 + 0.5625 t = -1.370732012 + 0.5625 Combine like terms: -1.370732012 + 0.5625 = -0.808232012 t = -0.808232012 Simplifying t = -0.808232012Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.933232012, -0.808232012}
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