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Simplifying 74.8t2 + 676.6666t + 464 = 0 Reorder the terms: 464 + 676.6666t + 74.8t2 = 0 Solving 464 + 676.6666t + 74.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 74.8 the coefficient of the squared term: Divide each side by '74.8'. 6.203208556 + 9.04634492t + t2 = 0 Move the constant term to the right: Add '-6.203208556' to each side of the equation. 6.203208556 + 9.04634492t + -6.203208556 + t2 = 0 + -6.203208556 Reorder the terms: 6.203208556 + -6.203208556 + 9.04634492t + t2 = 0 + -6.203208556 Combine like terms: 6.203208556 + -6.203208556 = 0.000000000 0.000000000 + 9.04634492t + t2 = 0 + -6.203208556 9.04634492t + t2 = 0 + -6.203208556 Combine like terms: 0 + -6.203208556 = -6.203208556 9.04634492t + t2 = -6.203208556 The t term is 9.04634492t. Take half its coefficient (4.52317246). Square it (20.45908910) and add it to both sides. Add '20.45908910' to each side of the equation. 9.04634492t + 20.45908910 + t2 = -6.203208556 + 20.45908910 Reorder the terms: 20.45908910 + 9.04634492t + t2 = -6.203208556 + 20.45908910 Combine like terms: -6.203208556 + 20.45908910 = 14.255880544 20.45908910 + 9.04634492t + t2 = 14.255880544 Factor a perfect square on the left side: (t + 4.52317246)(t + 4.52317246) = 14.255880544 Calculate the square root of the right side: 3.775696034 Break this problem into two subproblems by setting (t + 4.52317246) equal to 3.775696034 and -3.775696034.Subproblem 1
t + 4.52317246 = 3.775696034 Simplifying t + 4.52317246 = 3.775696034 Reorder the terms: 4.52317246 + t = 3.775696034 Solving 4.52317246 + t = 3.775696034 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.52317246' to each side of the equation. 4.52317246 + -4.52317246 + t = 3.775696034 + -4.52317246 Combine like terms: 4.52317246 + -4.52317246 = 0.00000000 0.00000000 + t = 3.775696034 + -4.52317246 t = 3.775696034 + -4.52317246 Combine like terms: 3.775696034 + -4.52317246 = -0.747476426 t = -0.747476426 Simplifying t = -0.747476426Subproblem 2
t + 4.52317246 = -3.775696034 Simplifying t + 4.52317246 = -3.775696034 Reorder the terms: 4.52317246 + t = -3.775696034 Solving 4.52317246 + t = -3.775696034 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.52317246' to each side of the equation. 4.52317246 + -4.52317246 + t = -3.775696034 + -4.52317246 Combine like terms: 4.52317246 + -4.52317246 = 0.00000000 0.00000000 + t = -3.775696034 + -4.52317246 t = -3.775696034 + -4.52317246 Combine like terms: -3.775696034 + -4.52317246 = -8.298868494 t = -8.298868494 Simplifying t = -8.298868494Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.747476426, -8.298868494}
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