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Simplifying 2000 = -16t2 + 500t + 5 Reorder the terms: 2000 = 5 + 500t + -16t2 Solving 2000 = 5 + 500t + -16t2 Solving for variable 't'. Combine like terms: 2000 + -5 = 1995 1995 + -500t + 16t2 = 5 + 500t + -16t2 + -5 + -500t + 16t2 Reorder the terms: 1995 + -500t + 16t2 = 5 + -5 + 500t + -500t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 1995 + -500t + 16t2 = 0 + 500t + -500t + -16t2 + 16t2 1995 + -500t + 16t2 = 500t + -500t + -16t2 + 16t2 Combine like terms: 500t + -500t = 0 1995 + -500t + 16t2 = 0 + -16t2 + 16t2 1995 + -500t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1995 + -500t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 124.6875 + -31.25t + t2 = 0 Move the constant term to the right: Add '-124.6875' to each side of the equation. 124.6875 + -31.25t + -124.6875 + t2 = 0 + -124.6875 Reorder the terms: 124.6875 + -124.6875 + -31.25t + t2 = 0 + -124.6875 Combine like terms: 124.6875 + -124.6875 = 0.0000 0.0000 + -31.25t + t2 = 0 + -124.6875 -31.25t + t2 = 0 + -124.6875 Combine like terms: 0 + -124.6875 = -124.6875 -31.25t + t2 = -124.6875 The t term is -31.25t. Take half its coefficient (-15.625). Square it (244.140625) and add it to both sides. Add '244.140625' to each side of the equation. -31.25t + 244.140625 + t2 = -124.6875 + 244.140625 Reorder the terms: 244.140625 + -31.25t + t2 = -124.6875 + 244.140625 Combine like terms: -124.6875 + 244.140625 = 119.453125 244.140625 + -31.25t + t2 = 119.453125 Factor a perfect square on the left side: (t + -15.625)(t + -15.625) = 119.453125 Calculate the square root of the right side: 10.929461332 Break this problem into two subproblems by setting (t + -15.625) equal to 10.929461332 and -10.929461332.Subproblem 1
t + -15.625 = 10.929461332 Simplifying t + -15.625 = 10.929461332 Reorder the terms: -15.625 + t = 10.929461332 Solving -15.625 + t = 10.929461332 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + t = 10.929461332 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + t = 10.929461332 + 15.625 t = 10.929461332 + 15.625 Combine like terms: 10.929461332 + 15.625 = 26.554461332 t = 26.554461332 Simplifying t = 26.554461332Subproblem 2
t + -15.625 = -10.929461332 Simplifying t + -15.625 = -10.929461332 Reorder the terms: -15.625 + t = -10.929461332 Solving -15.625 + t = -10.929461332 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + t = -10.929461332 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + t = -10.929461332 + 15.625 t = -10.929461332 + 15.625 Combine like terms: -10.929461332 + 15.625 = 4.695538668 t = 4.695538668 Simplifying t = 4.695538668Solution
The solution to the problem is based on the solutions from the subproblems. t = {26.554461332, 4.695538668}
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