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Simplifying 40 = 4.9t2 + 19t Reorder the terms: 40 = 19t + 4.9t2 Solving 40 = 19t + 4.9t2 Solving for variable 't'. Reorder the terms: 40 + -19t + -4.9t2 = 19t + -19t + 4.9t2 + -4.9t2 Combine like terms: 19t + -19t = 0 40 + -19t + -4.9t2 = 0 + 4.9t2 + -4.9t2 40 + -19t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 40 + -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'. -8.163265306 + 3.87755102t + t2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + 3.87755102t + 8.163265306 + t2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + 3.87755102t + t2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + 3.87755102t + t2 = 0 + 8.163265306 3.87755102t + t2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 3.87755102t + t2 = 8.163265306 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 = 8.163265306 + 3.758850478 Reorder the terms: 3.758850478 + 3.87755102t + t2 = 8.163265306 + 3.758850478 Combine like terms: 8.163265306 + 3.758850478 = 11.922115784 3.758850478 + 3.87755102t + t2 = 11.922115784 Factor a perfect square on the left side: (t + 1.93877551)(t + 1.93877551) = 11.922115784 Calculate the square root of the right side: 3.452841697 Break this problem into two subproblems by setting (t + 1.93877551) equal to 3.452841697 and -3.452841697.Subproblem 1
t + 1.93877551 = 3.452841697 Simplifying t + 1.93877551 = 3.452841697 Reorder the terms: 1.93877551 + t = 3.452841697 Solving 1.93877551 + t = 3.452841697 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 = 3.452841697 + -1.93877551 Combine like terms: 1.93877551 + -1.93877551 = 0.00000000 0.00000000 + t = 3.452841697 + -1.93877551 t = 3.452841697 + -1.93877551 Combine like terms: 3.452841697 + -1.93877551 = 1.514066187 t = 1.514066187 Simplifying t = 1.514066187Subproblem 2
t + 1.93877551 = -3.452841697 Simplifying t + 1.93877551 = -3.452841697 Reorder the terms: 1.93877551 + t = -3.452841697 Solving 1.93877551 + t = -3.452841697 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 = -3.452841697 + -1.93877551 Combine like terms: 1.93877551 + -1.93877551 = 0.00000000 0.00000000 + t = -3.452841697 + -1.93877551 t = -3.452841697 + -1.93877551 Combine like terms: -3.452841697 + -1.93877551 = -5.391617207 t = -5.391617207 Simplifying t = -5.391617207Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.514066187, -5.391617207}
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