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Simplifying 0 = 1.2t2 + -16.29t + 4.8 Reorder the terms: 0 = 4.8 + -16.29t + 1.2t2 Solving 0 = 4.8 + -16.29t + 1.2t2 Solving for variable 't'. Combine like terms: 0 + -4.8 = -4.8 -4.8 + 16.29t + -1.2t2 = 4.8 + -16.29t + 1.2t2 + -4.8 + 16.29t + -1.2t2 Reorder the terms: -4.8 + 16.29t + -1.2t2 = 4.8 + -4.8 + -16.29t + 16.29t + 1.2t2 + -1.2t2 Combine like terms: 4.8 + -4.8 = 0.0 -4.8 + 16.29t + -1.2t2 = 0.0 + -16.29t + 16.29t + 1.2t2 + -1.2t2 -4.8 + 16.29t + -1.2t2 = -16.29t + 16.29t + 1.2t2 + -1.2t2 Combine like terms: -16.29t + 16.29t = 0.00 -4.8 + 16.29t + -1.2t2 = 0.00 + 1.2t2 + -1.2t2 -4.8 + 16.29t + -1.2t2 = 1.2t2 + -1.2t2 Combine like terms: 1.2t2 + -1.2t2 = 0.0 -4.8 + 16.29t + -1.2t2 = 0.0 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. 4 + -13.575t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -13.575t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -13.575t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -13.575t + t2 = 0 + -4 -13.575t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -13.575t + t2 = -4 The t term is -13.575t. Take half its coefficient (-6.7875). Square it (46.07015625) and add it to both sides. Add '46.07015625' to each side of the equation. -13.575t + 46.07015625 + t2 = -4 + 46.07015625 Reorder the terms: 46.07015625 + -13.575t + t2 = -4 + 46.07015625 Combine like terms: -4 + 46.07015625 = 42.07015625 46.07015625 + -13.575t + t2 = 42.07015625 Factor a perfect square on the left side: (t + -6.7875)(t + -6.7875) = 42.07015625 Calculate the square root of the right side: 6.486151112 Break this problem into two subproblems by setting (t + -6.7875) equal to 6.486151112 and -6.486151112.Subproblem 1
t + -6.7875 = 6.486151112 Simplifying t + -6.7875 = 6.486151112 Reorder the terms: -6.7875 + t = 6.486151112 Solving -6.7875 + t = 6.486151112 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.7875' to each side of the equation. -6.7875 + 6.7875 + t = 6.486151112 + 6.7875 Combine like terms: -6.7875 + 6.7875 = 0.0000 0.0000 + t = 6.486151112 + 6.7875 t = 6.486151112 + 6.7875 Combine like terms: 6.486151112 + 6.7875 = 13.273651112 t = 13.273651112 Simplifying t = 13.273651112Subproblem 2
t + -6.7875 = -6.486151112 Simplifying t + -6.7875 = -6.486151112 Reorder the terms: -6.7875 + t = -6.486151112 Solving -6.7875 + t = -6.486151112 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.7875' to each side of the equation. -6.7875 + 6.7875 + t = -6.486151112 + 6.7875 Combine like terms: -6.7875 + 6.7875 = 0.0000 0.0000 + t = -6.486151112 + 6.7875 t = -6.486151112 + 6.7875 Combine like terms: -6.486151112 + 6.7875 = 0.301348888 t = 0.301348888 Simplifying t = 0.301348888Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.273651112, 0.301348888}
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