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Simplifying 0.0000408t2 + -0.00704t + 0.0807 = 0 Reorder the terms: 0.0807 + -0.00704t + 0.0000408t2 = 0 Solving 0.0807 + -0.00704t + 0.0000408t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0000408 the coefficient of the squared term: Divide each side by '0.0000408'. 1977.941176 + -172.5490196t + t2 = 0 Move the constant term to the right: Add '-1977.941176' to each side of the equation. 1977.941176 + -172.5490196t + -1977.941176 + t2 = 0 + -1977.941176 Reorder the terms: 1977.941176 + -1977.941176 + -172.5490196t + t2 = 0 + -1977.941176 Combine like terms: 1977.941176 + -1977.941176 = 0.000000 0.000000 + -172.5490196t + t2 = 0 + -1977.941176 -172.5490196t + t2 = 0 + -1977.941176 Combine like terms: 0 + -1977.941176 = -1977.941176 -172.5490196t + t2 = -1977.941176 The t term is -172.5490196t. Take half its coefficient (-86.2745098). Square it (7443.291041) and add it to both sides. Add '7443.291041' to each side of the equation. -172.5490196t + 7443.291041 + t2 = -1977.941176 + 7443.291041 Reorder the terms: 7443.291041 + -172.5490196t + t2 = -1977.941176 + 7443.291041 Combine like terms: -1977.941176 + 7443.291041 = 5465.349865 7443.291041 + -172.5490196t + t2 = 5465.349865 Factor a perfect square on the left side: (t + -86.2745098)(t + -86.2745098) = 5465.349865 Calculate the square root of the right side: 73.928004606 Break this problem into two subproblems by setting (t + -86.2745098) equal to 73.928004606 and -73.928004606.Subproblem 1
t + -86.2745098 = 73.928004606 Simplifying t + -86.2745098 = 73.928004606 Reorder the terms: -86.2745098 + t = 73.928004606 Solving -86.2745098 + t = 73.928004606 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '86.2745098' to each side of the equation. -86.2745098 + 86.2745098 + t = 73.928004606 + 86.2745098 Combine like terms: -86.2745098 + 86.2745098 = 0.0000000 0.0000000 + t = 73.928004606 + 86.2745098 t = 73.928004606 + 86.2745098 Combine like terms: 73.928004606 + 86.2745098 = 160.202514406 t = 160.202514406 Simplifying t = 160.202514406Subproblem 2
t + -86.2745098 = -73.928004606 Simplifying t + -86.2745098 = -73.928004606 Reorder the terms: -86.2745098 + t = -73.928004606 Solving -86.2745098 + t = -73.928004606 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '86.2745098' to each side of the equation. -86.2745098 + 86.2745098 + t = -73.928004606 + 86.2745098 Combine like terms: -86.2745098 + 86.2745098 = 0.0000000 0.0000000 + t = -73.928004606 + 86.2745098 t = -73.928004606 + 86.2745098 Combine like terms: -73.928004606 + 86.2745098 = 12.346505194 t = 12.346505194 Simplifying t = 12.346505194Solution
The solution to the problem is based on the solutions from the subproblems. t = {160.202514406, 12.346505194}
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