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Simplifying 0 = 4.9t2 + -19t + 11 Reorder the terms: 0 = 11 + -19t + 4.9t2 Solving 0 = 11 + -19t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -11 = -11 -11 + 19t + -4.9t2 = 11 + -19t + 4.9t2 + -11 + 19t + -4.9t2 Reorder the terms: -11 + 19t + -4.9t2 = 11 + -11 + -19t + 19t + 4.9t2 + -4.9t2 Combine like terms: 11 + -11 = 0 -11 + 19t + -4.9t2 = 0 + -19t + 19t + 4.9t2 + -4.9t2 -11 + 19t + -4.9t2 = -19t + 19t + 4.9t2 + -4.9t2 Combine like terms: -19t + 19t = 0 -11 + 19t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -11 + 19t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -11 + 19t + -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'. 2.244897959 + -3.87755102t + t2 = 0 Move the constant term to the right: Add '-2.244897959' to each side of the equation. 2.244897959 + -3.87755102t + -2.244897959 + t2 = 0 + -2.244897959 Reorder the terms: 2.244897959 + -2.244897959 + -3.87755102t + t2 = 0 + -2.244897959 Combine like terms: 2.244897959 + -2.244897959 = 0.000000000 0.000000000 + -3.87755102t + t2 = 0 + -2.244897959 -3.87755102t + t2 = 0 + -2.244897959 Combine like terms: 0 + -2.244897959 = -2.244897959 -3.87755102t + t2 = -2.244897959 The t term is -3.87755102t. Take half its coefficient (-1.93877551). Square it (3.758850478) and add it to both sides. Add '3.758850478' to each side of the equation. -3.87755102t + 3.758850478 + t2 = -2.244897959 + 3.758850478 Reorder the terms: 3.758850478 + -3.87755102t + t2 = -2.244897959 + 3.758850478 Combine like terms: -2.244897959 + 3.758850478 = 1.513952519 3.758850478 + -3.87755102t + t2 = 1.513952519 Factor a perfect square on the left side: (t + -1.93877551)(t + -1.93877551) = 1.513952519 Calculate the square root of the right side: 1.230427779 Break this problem into two subproblems by setting (t + -1.93877551) equal to 1.230427779 and -1.230427779.Subproblem 1
t + -1.93877551 = 1.230427779 Simplifying t + -1.93877551 = 1.230427779 Reorder the terms: -1.93877551 + t = 1.230427779 Solving -1.93877551 + t = 1.230427779 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.93877551' to each side of the equation. -1.93877551 + 1.93877551 + t = 1.230427779 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = 1.230427779 + 1.93877551 t = 1.230427779 + 1.93877551 Combine like terms: 1.230427779 + 1.93877551 = 3.169203289 t = 3.169203289 Simplifying t = 3.169203289Subproblem 2
t + -1.93877551 = -1.230427779 Simplifying t + -1.93877551 = -1.230427779 Reorder the terms: -1.93877551 + t = -1.230427779 Solving -1.93877551 + t = -1.230427779 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.93877551' to each side of the equation. -1.93877551 + 1.93877551 + t = -1.230427779 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = -1.230427779 + 1.93877551 t = -1.230427779 + 1.93877551 Combine like terms: -1.230427779 + 1.93877551 = 0.708347731 t = 0.708347731 Simplifying t = 0.708347731Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.169203289, 0.708347731}
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