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Simplifying (4.9t2) + 340t + -1768 = 0 Reorder the terms: -1768 + 340t + (4.9t2) = 0 Solving -1768 + 340t + (4.9t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -360.8163265 + 69.3877551t + t2 = 0 Move the constant term to the right: Add '360.8163265' to each side of the equation. -360.8163265 + 69.3877551t + 360.8163265 + t2 = 0 + 360.8163265 Reorder the terms: -360.8163265 + 360.8163265 + 69.3877551t + t2 = 0 + 360.8163265 Combine like terms: -360.8163265 + 360.8163265 = 0.0000000 0.0000000 + 69.3877551t + t2 = 0 + 360.8163265 69.3877551t + t2 = 0 + 360.8163265 Combine like terms: 0 + 360.8163265 = 360.8163265 69.3877551t + t2 = 360.8163265 The t term is 69.3877551t. Take half its coefficient (34.69387755). Square it (1203.665139) and add it to both sides. Add '1203.665139' to each side of the equation. 69.3877551t + 1203.665139 + t2 = 360.8163265 + 1203.665139 Reorder the terms: 1203.665139 + 69.3877551t + t2 = 360.8163265 + 1203.665139 Combine like terms: 360.8163265 + 1203.665139 = 1564.4814655 1203.665139 + 69.3877551t + t2 = 1564.4814655 Factor a perfect square on the left side: ((t) + 34.69387755)((t) + 34.69387755) = 1564.4814655 Calculate the square root of the right side: 39.553526587 Break this problem into two subproblems by setting ((t) + 34.69387755) equal to 39.553526587 and -39.553526587.Subproblem 1
(t) + 34.69387755 = 39.553526587 Simplifying (t) + 34.69387755 = 39.553526587 t + 34.69387755 = 39.553526587 Reorder the terms: 34.69387755 + t = 39.553526587 Solving 34.69387755 + t = 39.553526587 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-34.69387755' to each side of the equation. 34.69387755 + -34.69387755 + t = 39.553526587 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + t = 39.553526587 + -34.69387755 t = 39.553526587 + -34.69387755 Combine like terms: 39.553526587 + -34.69387755 = 4.859649037 t = 4.859649037 Simplifying t = 4.859649037Subproblem 2
(t) + 34.69387755 = -39.553526587 Simplifying (t) + 34.69387755 = -39.553526587 t + 34.69387755 = -39.553526587 Reorder the terms: 34.69387755 + t = -39.553526587 Solving 34.69387755 + t = -39.553526587 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-34.69387755' to each side of the equation. 34.69387755 + -34.69387755 + t = -39.553526587 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + t = -39.553526587 + -34.69387755 t = -39.553526587 + -34.69387755 Combine like terms: -39.553526587 + -34.69387755 = -74.247404137 t = -74.247404137 Simplifying t = -74.247404137Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.859649037, -74.247404137}
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