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Simplifying 49t2 + 760t + -35100 = 0 Reorder the terms: -35100 + 760t + 49t2 = 0 Solving -35100 + 760t + 49t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -716.3265306 + 15.51020408t + t2 = 0 Move the constant term to the right: Add '716.3265306' to each side of the equation. -716.3265306 + 15.51020408t + 716.3265306 + t2 = 0 + 716.3265306 Reorder the terms: -716.3265306 + 716.3265306 + 15.51020408t + t2 = 0 + 716.3265306 Combine like terms: -716.3265306 + 716.3265306 = 0.0000000 0.0000000 + 15.51020408t + t2 = 0 + 716.3265306 15.51020408t + t2 = 0 + 716.3265306 Combine like terms: 0 + 716.3265306 = 716.3265306 15.51020408t + t2 = 716.3265306 The t term is 15.51020408t. Take half its coefficient (7.75510204). Square it (60.14160765) and add it to both sides. Add '60.14160765' to each side of the equation. 15.51020408t + 60.14160765 + t2 = 716.3265306 + 60.14160765 Reorder the terms: 60.14160765 + 15.51020408t + t2 = 716.3265306 + 60.14160765 Combine like terms: 716.3265306 + 60.14160765 = 776.46813825 60.14160765 + 15.51020408t + t2 = 776.46813825 Factor a perfect square on the left side: (t + 7.75510204)(t + 7.75510204) = 776.46813825 Calculate the square root of the right side: 27.865177879 Break this problem into two subproblems by setting (t + 7.75510204) equal to 27.865177879 and -27.865177879.Subproblem 1
t + 7.75510204 = 27.865177879 Simplifying t + 7.75510204 = 27.865177879 Reorder the terms: 7.75510204 + t = 27.865177879 Solving 7.75510204 + t = 27.865177879 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.75510204' to each side of the equation. 7.75510204 + -7.75510204 + t = 27.865177879 + -7.75510204 Combine like terms: 7.75510204 + -7.75510204 = 0.00000000 0.00000000 + t = 27.865177879 + -7.75510204 t = 27.865177879 + -7.75510204 Combine like terms: 27.865177879 + -7.75510204 = 20.110075839 t = 20.110075839 Simplifying t = 20.110075839Subproblem 2
t + 7.75510204 = -27.865177879 Simplifying t + 7.75510204 = -27.865177879 Reorder the terms: 7.75510204 + t = -27.865177879 Solving 7.75510204 + t = -27.865177879 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.75510204' to each side of the equation. 7.75510204 + -7.75510204 + t = -27.865177879 + -7.75510204 Combine like terms: 7.75510204 + -7.75510204 = 0.00000000 0.00000000 + t = -27.865177879 + -7.75510204 t = -27.865177879 + -7.75510204 Combine like terms: -27.865177879 + -7.75510204 = -35.620279919 t = -35.620279919 Simplifying t = -35.620279919Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.110075839, -35.620279919}
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