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Simplifying 4.9t2 + -19t + -1.8 = 0 Reorder the terms: -1.8 + -19t + 4.9t2 = 0 Solving -1.8 + -19t + 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'. -0.3673469388 + -3.87755102t + t2 = 0 Move the constant term to the right: Add '0.3673469388' to each side of the equation. -0.3673469388 + -3.87755102t + 0.3673469388 + t2 = 0 + 0.3673469388 Reorder the terms: -0.3673469388 + 0.3673469388 + -3.87755102t + t2 = 0 + 0.3673469388 Combine like terms: -0.3673469388 + 0.3673469388 = 0.0000000000 0.0000000000 + -3.87755102t + t2 = 0 + 0.3673469388 -3.87755102t + t2 = 0 + 0.3673469388 Combine like terms: 0 + 0.3673469388 = 0.3673469388 -3.87755102t + t2 = 0.3673469388 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 = 0.3673469388 + 3.758850478 Reorder the terms: 3.758850478 + -3.87755102t + t2 = 0.3673469388 + 3.758850478 Combine like terms: 0.3673469388 + 3.758850478 = 4.1261974168 3.758850478 + -3.87755102t + t2 = 4.1261974168 Factor a perfect square on the left side: (t + -1.93877551)(t + -1.93877551) = 4.1261974168 Calculate the square root of the right side: 2.031304363 Break this problem into two subproblems by setting (t + -1.93877551) equal to 2.031304363 and -2.031304363.Subproblem 1
t + -1.93877551 = 2.031304363 Simplifying t + -1.93877551 = 2.031304363 Reorder the terms: -1.93877551 + t = 2.031304363 Solving -1.93877551 + t = 2.031304363 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 = 2.031304363 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = 2.031304363 + 1.93877551 t = 2.031304363 + 1.93877551 Combine like terms: 2.031304363 + 1.93877551 = 3.970079873 t = 3.970079873 Simplifying t = 3.970079873Subproblem 2
t + -1.93877551 = -2.031304363 Simplifying t + -1.93877551 = -2.031304363 Reorder the terms: -1.93877551 + t = -2.031304363 Solving -1.93877551 + t = -2.031304363 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 = -2.031304363 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = -2.031304363 + 1.93877551 t = -2.031304363 + 1.93877551 Combine like terms: -2.031304363 + 1.93877551 = -0.092528853 t = -0.092528853 Simplifying t = -0.092528853Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.970079873, -0.092528853}
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