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Simplifying 16.1t2 + 40t + 6 = 0 Reorder the terms: 6 + 40t + 16.1t2 = 0 Solving 6 + 40t + 16.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16.1 the coefficient of the squared term: Divide each side by '16.1'. 0.3726708075 + 2.48447205t + t2 = 0 Move the constant term to the right: Add '-0.3726708075' to each side of the equation. 0.3726708075 + 2.48447205t + -0.3726708075 + t2 = 0 + -0.3726708075 Reorder the terms: 0.3726708075 + -0.3726708075 + 2.48447205t + t2 = 0 + -0.3726708075 Combine like terms: 0.3726708075 + -0.3726708075 = 0.0000000000 0.0000000000 + 2.48447205t + t2 = 0 + -0.3726708075 2.48447205t + t2 = 0 + -0.3726708075 Combine like terms: 0 + -0.3726708075 = -0.3726708075 2.48447205t + t2 = -0.3726708075 The t term is 2.48447205t. Take half its coefficient (1.242236025). Square it (1.543150342) and add it to both sides. Add '1.543150342' to each side of the equation. 2.48447205t + 1.543150342 + t2 = -0.3726708075 + 1.543150342 Reorder the terms: 1.543150342 + 2.48447205t + t2 = -0.3726708075 + 1.543150342 Combine like terms: -0.3726708075 + 1.543150342 = 1.1704795345 1.543150342 + 2.48447205t + t2 = 1.1704795345 Factor a perfect square on the left side: (t + 1.242236025)(t + 1.242236025) = 1.1704795345 Calculate the square root of the right side: 1.081887025 Break this problem into two subproblems by setting (t + 1.242236025) equal to 1.081887025 and -1.081887025.Subproblem 1
t + 1.242236025 = 1.081887025 Simplifying t + 1.242236025 = 1.081887025 Reorder the terms: 1.242236025 + t = 1.081887025 Solving 1.242236025 + t = 1.081887025 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.242236025' to each side of the equation. 1.242236025 + -1.242236025 + t = 1.081887025 + -1.242236025 Combine like terms: 1.242236025 + -1.242236025 = 0.000000000 0.000000000 + t = 1.081887025 + -1.242236025 t = 1.081887025 + -1.242236025 Combine like terms: 1.081887025 + -1.242236025 = -0.160349 t = -0.160349 Simplifying t = -0.160349Subproblem 2
t + 1.242236025 = -1.081887025 Simplifying t + 1.242236025 = -1.081887025 Reorder the terms: 1.242236025 + t = -1.081887025 Solving 1.242236025 + t = -1.081887025 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.242236025' to each side of the equation. 1.242236025 + -1.242236025 + t = -1.081887025 + -1.242236025 Combine like terms: 1.242236025 + -1.242236025 = 0.000000000 0.000000000 + t = -1.081887025 + -1.242236025 t = -1.081887025 + -1.242236025 Combine like terms: -1.081887025 + -1.242236025 = -2.32412305 t = -2.32412305 Simplifying t = -2.32412305Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.160349, -2.32412305}
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