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Simplifying 4.9t2 + 340t + -2176 = 0 Reorder the terms: -2176 + 340t + 4.9t2 = 0 Solving -2176 + 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'. -444.0816327 + 69.3877551t + t2 = 0 Move the constant term to the right: Add '444.0816327' to each side of the equation. -444.0816327 + 69.3877551t + 444.0816327 + t2 = 0 + 444.0816327 Reorder the terms: -444.0816327 + 444.0816327 + 69.3877551t + t2 = 0 + 444.0816327 Combine like terms: -444.0816327 + 444.0816327 = 0.0000000 0.0000000 + 69.3877551t + t2 = 0 + 444.0816327 69.3877551t + t2 = 0 + 444.0816327 Combine like terms: 0 + 444.0816327 = 444.0816327 69.3877551t + t2 = 444.0816327 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 = 444.0816327 + 1203.665139 Reorder the terms: 1203.665139 + 69.3877551t + t2 = 444.0816327 + 1203.665139 Combine like terms: 444.0816327 + 1203.665139 = 1647.7467717 1203.665139 + 69.3877551t + t2 = 1647.7467717 Factor a perfect square on the left side: (t + 34.69387755)(t + 34.69387755) = 1647.7467717 Calculate the square root of the right side: 40.592447225 Break this problem into two subproblems by setting (t + 34.69387755) equal to 40.592447225 and -40.592447225.Subproblem 1
t + 34.69387755 = 40.592447225 Simplifying t + 34.69387755 = 40.592447225 Reorder the terms: 34.69387755 + t = 40.592447225 Solving 34.69387755 + t = 40.592447225 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 = 40.592447225 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + t = 40.592447225 + -34.69387755 t = 40.592447225 + -34.69387755 Combine like terms: 40.592447225 + -34.69387755 = 5.898569675 t = 5.898569675 Simplifying t = 5.898569675Subproblem 2
t + 34.69387755 = -40.592447225 Simplifying t + 34.69387755 = -40.592447225 Reorder the terms: 34.69387755 + t = -40.592447225 Solving 34.69387755 + t = -40.592447225 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 = -40.592447225 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + t = -40.592447225 + -34.69387755 t = -40.592447225 + -34.69387755 Combine like terms: -40.592447225 + -34.69387755 = -75.286324775 t = -75.286324775 Simplifying t = -75.286324775Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.898569675, -75.286324775}
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