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Simplifying 4.9t2 + -19.4t + 3.5 = 0 Reorder the terms: 3.5 + -19.4t + 4.9t2 = 0 Solving 3.5 + -19.4t + 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'. 0.7142857143 + -3.959183673t + t2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -3.959183673t + -0.7142857143 + t2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -3.959183673t + t2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -3.959183673t + t2 = 0 + -0.7142857143 -3.959183673t + t2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -3.959183673t + t2 = -0.7142857143 The t term is -3.959183673t. Take half its coefficient (-1.979591837). Square it (3.918783841) and add it to both sides. Add '3.918783841' to each side of the equation. -3.959183673t + 3.918783841 + t2 = -0.7142857143 + 3.918783841 Reorder the terms: 3.918783841 + -3.959183673t + t2 = -0.7142857143 + 3.918783841 Combine like terms: -0.7142857143 + 3.918783841 = 3.2044981267 3.918783841 + -3.959183673t + t2 = 3.2044981267 Factor a perfect square on the left side: (t + -1.979591837)(t + -1.979591837) = 3.2044981267 Calculate the square root of the right side: 1.790111205 Break this problem into two subproblems by setting (t + -1.979591837) equal to 1.790111205 and -1.790111205.Subproblem 1
t + -1.979591837 = 1.790111205 Simplifying t + -1.979591837 = 1.790111205 Reorder the terms: -1.979591837 + t = 1.790111205 Solving -1.979591837 + t = 1.790111205 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.979591837' to each side of the equation. -1.979591837 + 1.979591837 + t = 1.790111205 + 1.979591837 Combine like terms: -1.979591837 + 1.979591837 = 0.000000000 0.000000000 + t = 1.790111205 + 1.979591837 t = 1.790111205 + 1.979591837 Combine like terms: 1.790111205 + 1.979591837 = 3.769703042 t = 3.769703042 Simplifying t = 3.769703042Subproblem 2
t + -1.979591837 = -1.790111205 Simplifying t + -1.979591837 = -1.790111205 Reorder the terms: -1.979591837 + t = -1.790111205 Solving -1.979591837 + t = -1.790111205 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.979591837' to each side of the equation. -1.979591837 + 1.979591837 + t = -1.790111205 + 1.979591837 Combine like terms: -1.979591837 + 1.979591837 = 0.000000000 0.000000000 + t = -1.790111205 + 1.979591837 t = -1.790111205 + 1.979591837 Combine like terms: -1.790111205 + 1.979591837 = 0.189480632 t = 0.189480632 Simplifying t = 0.189480632Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.769703042, 0.189480632}
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