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Simplifying 16.0884t2 + 160t + -300 = 0 Reorder the terms: -300 + 160t + 16.0884t2 = 0 Solving -300 + 160t + 16.0884t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16.0884 the coefficient of the squared term: Divide each side by '16.0884'. -18.64697546 + 9.945053579t + t2 = 0 Move the constant term to the right: Add '18.64697546' to each side of the equation. -18.64697546 + 9.945053579t + 18.64697546 + t2 = 0 + 18.64697546 Reorder the terms: -18.64697546 + 18.64697546 + 9.945053579t + t2 = 0 + 18.64697546 Combine like terms: -18.64697546 + 18.64697546 = 0.00000000 0.00000000 + 9.945053579t + t2 = 0 + 18.64697546 9.945053579t + t2 = 0 + 18.64697546 Combine like terms: 0 + 18.64697546 = 18.64697546 9.945053579t + t2 = 18.64697546 The t term is 9.945053579t. Take half its coefficient (4.97252679). Square it (24.72602268) and add it to both sides. Add '24.72602268' to each side of the equation. 9.945053579t + 24.72602268 + t2 = 18.64697546 + 24.72602268 Reorder the terms: 24.72602268 + 9.945053579t + t2 = 18.64697546 + 24.72602268 Combine like terms: 18.64697546 + 24.72602268 = 43.37299814 24.72602268 + 9.945053579t + t2 = 43.37299814 Factor a perfect square on the left side: (t + 4.97252679)(t + 4.97252679) = 43.37299814 Calculate the square root of the right side: 6.585817955 Break this problem into two subproblems by setting (t + 4.97252679) equal to 6.585817955 and -6.585817955.Subproblem 1
t + 4.97252679 = 6.585817955 Simplifying t + 4.97252679 = 6.585817955 Reorder the terms: 4.97252679 + t = 6.585817955 Solving 4.97252679 + t = 6.585817955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.97252679' to each side of the equation. 4.97252679 + -4.97252679 + t = 6.585817955 + -4.97252679 Combine like terms: 4.97252679 + -4.97252679 = 0.00000000 0.00000000 + t = 6.585817955 + -4.97252679 t = 6.585817955 + -4.97252679 Combine like terms: 6.585817955 + -4.97252679 = 1.613291165 t = 1.613291165 Simplifying t = 1.613291165Subproblem 2
t + 4.97252679 = -6.585817955 Simplifying t + 4.97252679 = -6.585817955 Reorder the terms: 4.97252679 + t = -6.585817955 Solving 4.97252679 + t = -6.585817955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.97252679' to each side of the equation. 4.97252679 + -4.97252679 + t = -6.585817955 + -4.97252679 Combine like terms: 4.97252679 + -4.97252679 = 0.00000000 0.00000000 + t = -6.585817955 + -4.97252679 t = -6.585817955 + -4.97252679 Combine like terms: -6.585817955 + -4.97252679 = -11.558344745 t = -11.558344745 Simplifying t = -11.558344745Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.613291165, -11.558344745}
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