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Simplifying 8500 = -200t2 + 3600t Reorder the terms: 8500 = 3600t + -200t2 Solving 8500 = 3600t + -200t2 Solving for variable 't'. Reorder the terms: 8500 + -3600t + 200t2 = 3600t + -3600t + -200t2 + 200t2 Combine like terms: 3600t + -3600t = 0 8500 + -3600t + 200t2 = 0 + -200t2 + 200t2 8500 + -3600t + 200t2 = -200t2 + 200t2 Combine like terms: -200t2 + 200t2 = 0 8500 + -3600t + 200t2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(85 + -36t + 2t2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(85 + -36t + 2t2)' equal to zero and attempt to solve: Simplifying 85 + -36t + 2t2 = 0 Solving 85 + -36t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 42.5 + -18t + t2 = 0 Move the constant term to the right: Add '-42.5' to each side of the equation. 42.5 + -18t + -42.5 + t2 = 0 + -42.5 Reorder the terms: 42.5 + -42.5 + -18t + t2 = 0 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + -18t + t2 = 0 + -42.5 -18t + t2 = 0 + -42.5 Combine like terms: 0 + -42.5 = -42.5 -18t + t2 = -42.5 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = -42.5 + 81 Reorder the terms: 81 + -18t + t2 = -42.5 + 81 Combine like terms: -42.5 + 81 = 38.5 81 + -18t + t2 = 38.5 Factor a perfect square on the left side: (t + -9)(t + -9) = 38.5 Calculate the square root of the right side: 6.204836823 Break this problem into two subproblems by setting (t + -9) equal to 6.204836823 and -6.204836823.Subproblem 1
t + -9 = 6.204836823 Simplifying t + -9 = 6.204836823 Reorder the terms: -9 + t = 6.204836823 Solving -9 + t = 6.204836823 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 6.204836823 + 9 Combine like terms: -9 + 9 = 0 0 + t = 6.204836823 + 9 t = 6.204836823 + 9 Combine like terms: 6.204836823 + 9 = 15.204836823 t = 15.204836823 Simplifying t = 15.204836823Subproblem 2
t + -9 = -6.204836823 Simplifying t + -9 = -6.204836823 Reorder the terms: -9 + t = -6.204836823 Solving -9 + t = -6.204836823 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -6.204836823 + 9 Combine like terms: -9 + 9 = 0 0 + t = -6.204836823 + 9 t = -6.204836823 + 9 Combine like terms: -6.204836823 + 9 = 2.795163177 t = 2.795163177 Simplifying t = 2.795163177Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.204836823, 2.795163177}Solution
t = {15.204836823, 2.795163177}
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