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Simplifying -55 = -1.7t + -4.9t2 Solving -55 = -1.7t + -4.9t2 Solving for variable 't'. Reorder the terms: -55 + 1.7t + 4.9t2 = -1.7t + 1.7t + -4.9t2 + 4.9t2 Combine like terms: -1.7t + 1.7t = 0.0 -55 + 1.7t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -55 + 1.7t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -55 + 1.7t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -11.2244898 + 0.3469387755t + t2 = 0 Move the constant term to the right: Add '11.2244898' to each side of the equation. -11.2244898 + 0.3469387755t + 11.2244898 + t2 = 0 + 11.2244898 Reorder the terms: -11.2244898 + 11.2244898 + 0.3469387755t + t2 = 0 + 11.2244898 Combine like terms: -11.2244898 + 11.2244898 = 0.0000000 0.0000000 + 0.3469387755t + t2 = 0 + 11.2244898 0.3469387755t + t2 = 0 + 11.2244898 Combine like terms: 0 + 11.2244898 = 11.2244898 0.3469387755t + t2 = 11.2244898 The t term is 0.3469387755t. Take half its coefficient (0.1734693878). Square it (0.03009162850) and add it to both sides. Add '0.03009162850' to each side of the equation. 0.3469387755t + 0.03009162850 + t2 = 11.2244898 + 0.03009162850 Reorder the terms: 0.03009162850 + 0.3469387755t + t2 = 11.2244898 + 0.03009162850 Combine like terms: 11.2244898 + 0.03009162850 = 11.2545814285 0.03009162850 + 0.3469387755t + t2 = 11.2545814285 Factor a perfect square on the left side: (t + 0.1734693878)(t + 0.1734693878) = 11.2545814285 Calculate the square root of the right side: 3.354784856 Break this problem into two subproblems by setting (t + 0.1734693878) equal to 3.354784856 and -3.354784856.Subproblem 1
t + 0.1734693878 = 3.354784856 Simplifying t + 0.1734693878 = 3.354784856 Reorder the terms: 0.1734693878 + t = 3.354784856 Solving 0.1734693878 + t = 3.354784856 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1734693878' to each side of the equation. 0.1734693878 + -0.1734693878 + t = 3.354784856 + -0.1734693878 Combine like terms: 0.1734693878 + -0.1734693878 = 0.0000000000 0.0000000000 + t = 3.354784856 + -0.1734693878 t = 3.354784856 + -0.1734693878 Combine like terms: 3.354784856 + -0.1734693878 = 3.1813154682 t = 3.1813154682 Simplifying t = 3.1813154682Subproblem 2
t + 0.1734693878 = -3.354784856 Simplifying t + 0.1734693878 = -3.354784856 Reorder the terms: 0.1734693878 + t = -3.354784856 Solving 0.1734693878 + t = -3.354784856 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1734693878' to each side of the equation. 0.1734693878 + -0.1734693878 + t = -3.354784856 + -0.1734693878 Combine like terms: 0.1734693878 + -0.1734693878 = 0.0000000000 0.0000000000 + t = -3.354784856 + -0.1734693878 t = -3.354784856 + -0.1734693878 Combine like terms: -3.354784856 + -0.1734693878 = -3.5282542438 t = -3.5282542438 Simplifying t = -3.5282542438Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.1813154682, -3.5282542438}
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