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Simplifying 734t2 + -50000t + 650000 = 0 Reorder the terms: 650000 + -50000t + 734t2 = 0 Solving 650000 + -50000t + 734t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(325000 + -25000t + 367t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(325000 + -25000t + 367t2)' equal to zero and attempt to solve: Simplifying 325000 + -25000t + 367t2 = 0 Solving 325000 + -25000t + 367t2 = 0 Begin completing the square. Divide all terms by 367 the coefficient of the squared term: Divide each side by '367'. 885.5585831 + -68.11989101t + t2 = 0 Move the constant term to the right: Add '-885.5585831' to each side of the equation. 885.5585831 + -68.11989101t + -885.5585831 + t2 = 0 + -885.5585831 Reorder the terms: 885.5585831 + -885.5585831 + -68.11989101t + t2 = 0 + -885.5585831 Combine like terms: 885.5585831 + -885.5585831 = 0.0000000 0.0000000 + -68.11989101t + t2 = 0 + -885.5585831 -68.11989101t + t2 = 0 + -885.5585831 Combine like terms: 0 + -885.5585831 = -885.5585831 -68.11989101t + t2 = -885.5585831 The t term is -68.11989101t. Take half its coefficient (-34.05994551). Square it (1160.079888) and add it to both sides. Add '1160.079888' to each side of the equation. -68.11989101t + 1160.079888 + t2 = -885.5585831 + 1160.079888 Reorder the terms: 1160.079888 + -68.11989101t + t2 = -885.5585831 + 1160.079888 Combine like terms: -885.5585831 + 1160.079888 = 274.5213049 1160.079888 + -68.11989101t + t2 = 274.5213049 Factor a perfect square on the left side: (t + -34.05994551)(t + -34.05994551) = 274.5213049 Calculate the square root of the right side: 16.568684465 Break this problem into two subproblems by setting (t + -34.05994551) equal to 16.568684465 and -16.568684465.Subproblem 1
t + -34.05994551 = 16.568684465 Simplifying t + -34.05994551 = 16.568684465 Reorder the terms: -34.05994551 + t = 16.568684465 Solving -34.05994551 + t = 16.568684465 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '34.05994551' to each side of the equation. -34.05994551 + 34.05994551 + t = 16.568684465 + 34.05994551 Combine like terms: -34.05994551 + 34.05994551 = 0.00000000 0.00000000 + t = 16.568684465 + 34.05994551 t = 16.568684465 + 34.05994551 Combine like terms: 16.568684465 + 34.05994551 = 50.628629975 t = 50.628629975 Simplifying t = 50.628629975Subproblem 2
t + -34.05994551 = -16.568684465 Simplifying t + -34.05994551 = -16.568684465 Reorder the terms: -34.05994551 + t = -16.568684465 Solving -34.05994551 + t = -16.568684465 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '34.05994551' to each side of the equation. -34.05994551 + 34.05994551 + t = -16.568684465 + 34.05994551 Combine like terms: -34.05994551 + 34.05994551 = 0.00000000 0.00000000 + t = -16.568684465 + 34.05994551 t = -16.568684465 + 34.05994551 Combine like terms: -16.568684465 + 34.05994551 = 17.491261045 t = 17.491261045 Simplifying t = 17.491261045Solution
The solution to the problem is based on the solutions from the subproblems. t = {50.628629975, 17.491261045}Solution
t = {50.628629975, 17.491261045}
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