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Simplifying 4.9t2 + -16t + 5 = 0 Reorder the terms: 5 + -16t + 4.9t2 = 0 Solving 5 + -16t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 1.020408163 + -3.265306122t + t2 = 0 Move the constant term to the right: Add '-1.020408163' to each side of the equation. 1.020408163 + -3.265306122t + -1.020408163 + t2 = 0 + -1.020408163 Reorder the terms: 1.020408163 + -1.020408163 + -3.265306122t + t2 = 0 + -1.020408163 Combine like terms: 1.020408163 + -1.020408163 = 0.000000000 0.000000000 + -3.265306122t + t2 = 0 + -1.020408163 -3.265306122t + t2 = 0 + -1.020408163 Combine like terms: 0 + -1.020408163 = -1.020408163 -3.265306122t + t2 = -1.020408163 The t term is -3.265306122t. Take half its coefficient (-1.632653061). Square it (2.665556018) and add it to both sides. Add '2.665556018' to each side of the equation. -3.265306122t + 2.665556018 + t2 = -1.020408163 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122t + t2 = -1.020408163 + 2.665556018 Combine like terms: -1.020408163 + 2.665556018 = 1.645147855 2.665556018 + -3.265306122t + t2 = 1.645147855 Factor a perfect square on the left side: (t + -1.632653061)(t + -1.632653061) = 1.645147855 Calculate the square root of the right side: 1.282633172 Break this problem into two subproblems by setting (t + -1.632653061) equal to 1.282633172 and -1.282633172.Subproblem 1
t + -1.632653061 = 1.282633172 Simplifying t + -1.632653061 = 1.282633172 Reorder the terms: -1.632653061 + t = 1.282633172 Solving -1.632653061 + t = 1.282633172 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = 1.282633172 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 1.282633172 + 1.632653061 t = 1.282633172 + 1.632653061 Combine like terms: 1.282633172 + 1.632653061 = 2.915286233 t = 2.915286233 Simplifying t = 2.915286233Subproblem 2
t + -1.632653061 = -1.282633172 Simplifying t + -1.632653061 = -1.282633172 Reorder the terms: -1.632653061 + t = -1.282633172 Solving -1.632653061 + t = -1.282633172 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = -1.282633172 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -1.282633172 + 1.632653061 t = -1.282633172 + 1.632653061 Combine like terms: -1.282633172 + 1.632653061 = 0.350019889 t = 0.350019889 Simplifying t = 0.350019889Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.915286233, 0.350019889}
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