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Simplifying 4.9t2 + 340t + -2720 = 0 Reorder the terms: -2720 + 340t + 4.9t2 = 0 Solving -2720 + 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'. -555.1020408 + 69.3877551t + t2 = 0 Move the constant term to the right: Add '555.1020408' to each side of the equation. -555.1020408 + 69.3877551t + 555.1020408 + t2 = 0 + 555.1020408 Reorder the terms: -555.1020408 + 555.1020408 + 69.3877551t + t2 = 0 + 555.1020408 Combine like terms: -555.1020408 + 555.1020408 = 0.0000000 0.0000000 + 69.3877551t + t2 = 0 + 555.1020408 69.3877551t + t2 = 0 + 555.1020408 Combine like terms: 0 + 555.1020408 = 555.1020408 69.3877551t + t2 = 555.1020408 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 = 555.1020408 + 1203.665139 Reorder the terms: 1203.665139 + 69.3877551t + t2 = 555.1020408 + 1203.665139 Combine like terms: 555.1020408 + 1203.665139 = 1758.7671798 1203.665139 + 69.3877551t + t2 = 1758.7671798 Factor a perfect square on the left side: (t + 34.69387755)(t + 34.69387755) = 1758.7671798 Calculate the square root of the right side: 41.937658254 Break this problem into two subproblems by setting (t + 34.69387755) equal to 41.937658254 and -41.937658254.Subproblem 1
t + 34.69387755 = 41.937658254 Simplifying t + 34.69387755 = 41.937658254 Reorder the terms: 34.69387755 + t = 41.937658254 Solving 34.69387755 + t = 41.937658254 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 = 41.937658254 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + t = 41.937658254 + -34.69387755 t = 41.937658254 + -34.69387755 Combine like terms: 41.937658254 + -34.69387755 = 7.243780704 t = 7.243780704 Simplifying t = 7.243780704Subproblem 2
t + 34.69387755 = -41.937658254 Simplifying t + 34.69387755 = -41.937658254 Reorder the terms: 34.69387755 + t = -41.937658254 Solving 34.69387755 + t = -41.937658254 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 = -41.937658254 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + t = -41.937658254 + -34.69387755 t = -41.937658254 + -34.69387755 Combine like terms: -41.937658254 + -34.69387755 = -76.631535804 t = -76.631535804 Simplifying t = -76.631535804Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.243780704, -76.631535804}
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