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Simplifying 1341t + 8.2t2 = 40000 Solving 1341t + 8.2t2 = 40000 Solving for variable 't'. Reorder the terms: -40000 + 1341t + 8.2t2 = 40000 + -40000 Combine like terms: 40000 + -40000 = 0 -40000 + 1341t + 8.2t2 = 0 Begin completing the square. Divide all terms by 8.2 the coefficient of the squared term: Divide each side by '8.2'. -4878.04878 + 163.5365854t + t2 = 0 Move the constant term to the right: Add '4878.04878' to each side of the equation. -4878.04878 + 163.5365854t + 4878.04878 + t2 = 0 + 4878.04878 Reorder the terms: -4878.04878 + 4878.04878 + 163.5365854t + t2 = 0 + 4878.04878 Combine like terms: -4878.04878 + 4878.04878 = 0.00000 0.00000 + 163.5365854t + t2 = 0 + 4878.04878 163.5365854t + t2 = 0 + 4878.04878 Combine like terms: 0 + 4878.04878 = 4878.04878 163.5365854t + t2 = 4878.04878 The t term is 163.5365854t. Take half its coefficient (81.7682927). Square it (6686.053691) and add it to both sides. Add '6686.053691' to each side of the equation. 163.5365854t + 6686.053691 + t2 = 4878.04878 + 6686.053691 Reorder the terms: 6686.053691 + 163.5365854t + t2 = 4878.04878 + 6686.053691 Combine like terms: 4878.04878 + 6686.053691 = 11564.102471 6686.053691 + 163.5365854t + t2 = 11564.102471 Factor a perfect square on the left side: (t + 81.7682927)(t + 81.7682927) = 11564.102471 Calculate the square root of the right side: 107.536516919 Break this problem into two subproblems by setting (t + 81.7682927) equal to 107.536516919 and -107.536516919.Subproblem 1
t + 81.7682927 = 107.536516919 Simplifying t + 81.7682927 = 107.536516919 Reorder the terms: 81.7682927 + t = 107.536516919 Solving 81.7682927 + t = 107.536516919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-81.7682927' to each side of the equation. 81.7682927 + -81.7682927 + t = 107.536516919 + -81.7682927 Combine like terms: 81.7682927 + -81.7682927 = 0.0000000 0.0000000 + t = 107.536516919 + -81.7682927 t = 107.536516919 + -81.7682927 Combine like terms: 107.536516919 + -81.7682927 = 25.768224219 t = 25.768224219 Simplifying t = 25.768224219Subproblem 2
t + 81.7682927 = -107.536516919 Simplifying t + 81.7682927 = -107.536516919 Reorder the terms: 81.7682927 + t = -107.536516919 Solving 81.7682927 + t = -107.536516919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-81.7682927' to each side of the equation. 81.7682927 + -81.7682927 + t = -107.536516919 + -81.7682927 Combine like terms: 81.7682927 + -81.7682927 = 0.0000000 0.0000000 + t = -107.536516919 + -81.7682927 t = -107.536516919 + -81.7682927 Combine like terms: -107.536516919 + -81.7682927 = -189.304809619 t = -189.304809619 Simplifying t = -189.304809619Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.768224219, -189.304809619}
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