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Simplifying (4.9t2) + 340t + -1360 = 0 Reorder the terms: -1360 + 340t + (4.9t2) = 0 Solving -1360 + 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'. -277.5510204 + 69.3877551t + t2 = 0 Move the constant term to the right: Add '277.5510204' to each side of the equation. -277.5510204 + 69.3877551t + 277.5510204 + t2 = 0 + 277.5510204 Reorder the terms: -277.5510204 + 277.5510204 + 69.3877551t + t2 = 0 + 277.5510204 Combine like terms: -277.5510204 + 277.5510204 = 0.0000000 0.0000000 + 69.3877551t + t2 = 0 + 277.5510204 69.3877551t + t2 = 0 + 277.5510204 Combine like terms: 0 + 277.5510204 = 277.5510204 69.3877551t + t2 = 277.5510204 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 = 277.5510204 + 1203.665139 Reorder the terms: 1203.665139 + 69.3877551t + t2 = 277.5510204 + 1203.665139 Combine like terms: 277.5510204 + 1203.665139 = 1481.2161594 1203.665139 + 69.3877551t + t2 = 1481.2161594 Factor a perfect square on the left side: ((t) + 34.69387755)((t) + 34.69387755) = 1481.2161594 Calculate the square root of the right side: 38.486571157 Break this problem into two subproblems by setting ((t) + 34.69387755) equal to 38.486571157 and -38.486571157.Subproblem 1
(t) + 34.69387755 = 38.486571157 Simplifying (t) + 34.69387755 = 38.486571157 t + 34.69387755 = 38.486571157 Reorder the terms: 34.69387755 + t = 38.486571157 Solving 34.69387755 + t = 38.486571157 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 = 38.486571157 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + t = 38.486571157 + -34.69387755 t = 38.486571157 + -34.69387755 Combine like terms: 38.486571157 + -34.69387755 = 3.792693607 t = 3.792693607 Simplifying t = 3.792693607Subproblem 2
(t) + 34.69387755 = -38.486571157 Simplifying (t) + 34.69387755 = -38.486571157 t + 34.69387755 = -38.486571157 Reorder the terms: 34.69387755 + t = -38.486571157 Solving 34.69387755 + t = -38.486571157 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 = -38.486571157 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + t = -38.486571157 + -34.69387755 t = -38.486571157 + -34.69387755 Combine like terms: -38.486571157 + -34.69387755 = -73.180448707 t = -73.180448707 Simplifying t = -73.180448707Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.792693607, -73.180448707}
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