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Simplifying 25.6 = -0.08t2 + 9.6t Reorder the terms: 25.6 = 9.6t + -0.08t2 Solving 25.6 = 9.6t + -0.08t2 Solving for variable 't'. Reorder the terms: 25.6 + -9.6t + 0.08t2 = 9.6t + -9.6t + -0.08t2 + 0.08t2 Combine like terms: 9.6t + -9.6t = 0.0 25.6 + -9.6t + 0.08t2 = 0.0 + -0.08t2 + 0.08t2 25.6 + -9.6t + 0.08t2 = -0.08t2 + 0.08t2 Combine like terms: -0.08t2 + 0.08t2 = 0.00 25.6 + -9.6t + 0.08t2 = 0.00 Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. 320 + -120t + t2 = 0 Move the constant term to the right: Add '-320' to each side of the equation. 320 + -120t + -320 + t2 = 0 + -320 Reorder the terms: 320 + -320 + -120t + t2 = 0 + -320 Combine like terms: 320 + -320 = 0 0 + -120t + t2 = 0 + -320 -120t + t2 = 0 + -320 Combine like terms: 0 + -320 = -320 -120t + t2 = -320 The t term is -120t. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120t + 3600 + t2 = -320 + 3600 Reorder the terms: 3600 + -120t + t2 = -320 + 3600 Combine like terms: -320 + 3600 = 3280 3600 + -120t + t2 = 3280 Factor a perfect square on the left side: (t + -60)(t + -60) = 3280 Calculate the square root of the right side: 57.271284253 Break this problem into two subproblems by setting (t + -60) equal to 57.271284253 and -57.271284253.Subproblem 1
t + -60 = 57.271284253 Simplifying t + -60 = 57.271284253 Reorder the terms: -60 + t = 57.271284253 Solving -60 + t = 57.271284253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + t = 57.271284253 + 60 Combine like terms: -60 + 60 = 0 0 + t = 57.271284253 + 60 t = 57.271284253 + 60 Combine like terms: 57.271284253 + 60 = 117.271284253 t = 117.271284253 Simplifying t = 117.271284253Subproblem 2
t + -60 = -57.271284253 Simplifying t + -60 = -57.271284253 Reorder the terms: -60 + t = -57.271284253 Solving -60 + t = -57.271284253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + t = -57.271284253 + 60 Combine like terms: -60 + 60 = 0 0 + t = -57.271284253 + 60 t = -57.271284253 + 60 Combine like terms: -57.271284253 + 60 = 2.728715747 t = 2.728715747 Simplifying t = 2.728715747Solution
The solution to the problem is based on the solutions from the subproblems. t = {117.271284253, 2.728715747}
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