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Simplifying -16.1t2 + 40t + 4 = 0 Reorder the terms: 4 + 40t + -16.1t2 = 0 Solving 4 + 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'. -0.248447205 + -2.48447205t + t2 = 0 Move the constant term to the right: Add '0.248447205' to each side of the equation. -0.248447205 + -2.48447205t + 0.248447205 + t2 = 0 + 0.248447205 Reorder the terms: -0.248447205 + 0.248447205 + -2.48447205t + t2 = 0 + 0.248447205 Combine like terms: -0.248447205 + 0.248447205 = 0.000000000 0.000000000 + -2.48447205t + t2 = 0 + 0.248447205 -2.48447205t + t2 = 0 + 0.248447205 Combine like terms: 0 + 0.248447205 = 0.248447205 -2.48447205t + t2 = 0.248447205 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 = 0.248447205 + 1.543150342 Reorder the terms: 1.543150342 + -2.48447205t + t2 = 0.248447205 + 1.543150342 Combine like terms: 0.248447205 + 1.543150342 = 1.791597547 1.543150342 + -2.48447205t + t2 = 1.791597547 Factor a perfect square on the left side: (t + -1.242236025)(t + -1.242236025) = 1.791597547 Calculate the square root of the right side: 1.338505714 Break this problem into two subproblems by setting (t + -1.242236025) equal to 1.338505714 and -1.338505714.Subproblem 1
t + -1.242236025 = 1.338505714 Simplifying t + -1.242236025 = 1.338505714 Reorder the terms: -1.242236025 + t = 1.338505714 Solving -1.242236025 + t = 1.338505714 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 = 1.338505714 + 1.242236025 Combine like terms: -1.242236025 + 1.242236025 = 0.000000000 0.000000000 + t = 1.338505714 + 1.242236025 t = 1.338505714 + 1.242236025 Combine like terms: 1.338505714 + 1.242236025 = 2.580741739 t = 2.580741739 Simplifying t = 2.580741739Subproblem 2
t + -1.242236025 = -1.338505714 Simplifying t + -1.242236025 = -1.338505714 Reorder the terms: -1.242236025 + t = -1.338505714 Solving -1.242236025 + t = -1.338505714 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 = -1.338505714 + 1.242236025 Combine like terms: -1.242236025 + 1.242236025 = 0.000000000 0.000000000 + t = -1.338505714 + 1.242236025 t = -1.338505714 + 1.242236025 Combine like terms: -1.338505714 + 1.242236025 = -0.096269689 t = -0.096269689 Simplifying t = -0.096269689Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.580741739, -0.096269689}
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