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Simplifying -16.1(t * t) + 40t = 4 Multiply t * t -16.1(t2) + 40t = 4 Reorder the terms: 40t + -16.1t2 = 4 Solving 40t + -16.1t2 = 4 Solving for variable 't'. Reorder the terms: -4 + 40t + -16.1t2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 40t + -16.1t2 = 0 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 = 1.294703137 1.543150342 + -2.48447205t + t2 = 1.294703137 Factor a perfect square on the left side: (t + -1.242236025)(t + -1.242236025) = 1.294703137 Calculate the square root of the right side: 1.137850226 Break this problem into two subproblems by setting (t + -1.242236025) equal to 1.137850226 and -1.137850226.Subproblem 1
t + -1.242236025 = 1.137850226 Simplifying t + -1.242236025 = 1.137850226 Reorder the terms: -1.242236025 + t = 1.137850226 Solving -1.242236025 + t = 1.137850226 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 = 1.137850226 + 1.242236025 Combine like terms: -1.242236025 + 1.242236025 = 0.000000000 0.000000000 + t = 1.137850226 + 1.242236025 t = 1.137850226 + 1.242236025 Combine like terms: 1.137850226 + 1.242236025 = 2.380086251 t = 2.380086251 Simplifying t = 2.380086251Subproblem 2
t + -1.242236025 = -1.137850226 Simplifying t + -1.242236025 = -1.137850226 Reorder the terms: -1.242236025 + t = -1.137850226 Solving -1.242236025 + t = -1.137850226 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 = -1.137850226 + 1.242236025 Combine like terms: -1.242236025 + 1.242236025 = 0.000000000 0.000000000 + t = -1.137850226 + 1.242236025 t = -1.137850226 + 1.242236025 Combine like terms: -1.137850226 + 1.242236025 = 0.104385799 t = 0.104385799 Simplifying t = 0.104385799Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.380086251, 0.104385799}
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