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Simplifying 323.499t2 + -1942.738t + 2657.917 = 0 Reorder the terms: 2657.917 + -1942.738t + 323.499t2 = 0 Solving 2657.917 + -1942.738t + 323.499t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 323.499 the coefficient of the squared term: Divide each side by '323.499'. 8.216152136 + -6.005391052t + t2 = 0 Move the constant term to the right: Add '-8.216152136' to each side of the equation. 8.216152136 + -6.005391052t + -8.216152136 + t2 = 0 + -8.216152136 Reorder the terms: 8.216152136 + -8.216152136 + -6.005391052t + t2 = 0 + -8.216152136 Combine like terms: 8.216152136 + -8.216152136 = 0.000000000 0.000000000 + -6.005391052t + t2 = 0 + -8.216152136 -6.005391052t + t2 = 0 + -8.216152136 Combine like terms: 0 + -8.216152136 = -8.216152136 -6.005391052t + t2 = -8.216152136 The t term is -6.005391052t. Take half its coefficient (-3.002695526). Square it (9.016180422) and add it to both sides. Add '9.016180422' to each side of the equation. -6.005391052t + 9.016180422 + t2 = -8.216152136 + 9.016180422 Reorder the terms: 9.016180422 + -6.005391052t + t2 = -8.216152136 + 9.016180422 Combine like terms: -8.216152136 + 9.016180422 = 0.800028286 9.016180422 + -6.005391052t + t2 = 0.800028286 Factor a perfect square on the left side: (t + -3.002695526)(t + -3.002695526) = 0.800028286 Calculate the square root of the right side: 0.894443003 Break this problem into two subproblems by setting (t + -3.002695526) equal to 0.894443003 and -0.894443003.Subproblem 1
t + -3.002695526 = 0.894443003 Simplifying t + -3.002695526 = 0.894443003 Reorder the terms: -3.002695526 + t = 0.894443003 Solving -3.002695526 + t = 0.894443003 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.002695526' to each side of the equation. -3.002695526 + 3.002695526 + t = 0.894443003 + 3.002695526 Combine like terms: -3.002695526 + 3.002695526 = 0.000000000 0.000000000 + t = 0.894443003 + 3.002695526 t = 0.894443003 + 3.002695526 Combine like terms: 0.894443003 + 3.002695526 = 3.897138529 t = 3.897138529 Simplifying t = 3.897138529Subproblem 2
t + -3.002695526 = -0.894443003 Simplifying t + -3.002695526 = -0.894443003 Reorder the terms: -3.002695526 + t = -0.894443003 Solving -3.002695526 + t = -0.894443003 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.002695526' to each side of the equation. -3.002695526 + 3.002695526 + t = -0.894443003 + 3.002695526 Combine like terms: -3.002695526 + 3.002695526 = 0.000000000 0.000000000 + t = -0.894443003 + 3.002695526 t = -0.894443003 + 3.002695526 Combine like terms: -0.894443003 + 3.002695526 = 2.108252523 t = 2.108252523 Simplifying t = 2.108252523Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.897138529, 2.108252523}
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