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Simplifying 19.9908t2 + -135.9t + 124.8 = 0 Reorder the terms: 124.8 + -135.9t + 19.9908t2 = 0 Solving 124.8 + -135.9t + 19.9908t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 19.9908 the coefficient of the squared term: Divide each side by '19.9908'. 6.242871721 + -6.798127138t + t2 = 0 Move the constant term to the right: Add '-6.242871721' to each side of the equation. 6.242871721 + -6.798127138t + -6.242871721 + t2 = 0 + -6.242871721 Reorder the terms: 6.242871721 + -6.242871721 + -6.798127138t + t2 = 0 + -6.242871721 Combine like terms: 6.242871721 + -6.242871721 = 0.000000000 0.000000000 + -6.798127138t + t2 = 0 + -6.242871721 -6.798127138t + t2 = 0 + -6.242871721 Combine like terms: 0 + -6.242871721 = -6.242871721 -6.798127138t + t2 = -6.242871721 The t term is -6.798127138t. Take half its coefficient (-3.399063569). Square it (11.55363315) and add it to both sides. Add '11.55363315' to each side of the equation. -6.798127138t + 11.55363315 + t2 = -6.242871721 + 11.55363315 Reorder the terms: 11.55363315 + -6.798127138t + t2 = -6.242871721 + 11.55363315 Combine like terms: -6.242871721 + 11.55363315 = 5.310761429 11.55363315 + -6.798127138t + t2 = 5.310761429 Factor a perfect square on the left side: (t + -3.399063569)(t + -3.399063569) = 5.310761429 Calculate the square root of the right side: 2.304508934 Break this problem into two subproblems by setting (t + -3.399063569) equal to 2.304508934 and -2.304508934.Subproblem 1
t + -3.399063569 = 2.304508934 Simplifying t + -3.399063569 = 2.304508934 Reorder the terms: -3.399063569 + t = 2.304508934 Solving -3.399063569 + t = 2.304508934 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.399063569' to each side of the equation. -3.399063569 + 3.399063569 + t = 2.304508934 + 3.399063569 Combine like terms: -3.399063569 + 3.399063569 = 0.000000000 0.000000000 + t = 2.304508934 + 3.399063569 t = 2.304508934 + 3.399063569 Combine like terms: 2.304508934 + 3.399063569 = 5.703572503 t = 5.703572503 Simplifying t = 5.703572503Subproblem 2
t + -3.399063569 = -2.304508934 Simplifying t + -3.399063569 = -2.304508934 Reorder the terms: -3.399063569 + t = -2.304508934 Solving -3.399063569 + t = -2.304508934 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.399063569' to each side of the equation. -3.399063569 + 3.399063569 + t = -2.304508934 + 3.399063569 Combine like terms: -3.399063569 + 3.399063569 = 0.000000000 0.000000000 + t = -2.304508934 + 3.399063569 t = -2.304508934 + 3.399063569 Combine like terms: -2.304508934 + 3.399063569 = 1.094554635 t = 1.094554635 Simplifying t = 1.094554635Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.703572503, 1.094554635}
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