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Simplifying 80 = 137t + -4.9t2 Solving 80 = 137t + -4.9t2 Solving for variable 't'. Reorder the terms: 80 + -137t + 4.9t2 = 137t + -137t + -4.9t2 + 4.9t2 Combine like terms: 137t + -137t = 0 80 + -137t + 4.9t2 = 0 + -4.9t2 + 4.9t2 80 + -137t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 80 + -137t + 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'. 16.32653061 + -27.95918367t + t2 = 0 Move the constant term to the right: Add '-16.32653061' to each side of the equation. 16.32653061 + -27.95918367t + -16.32653061 + t2 = 0 + -16.32653061 Reorder the terms: 16.32653061 + -16.32653061 + -27.95918367t + t2 = 0 + -16.32653061 Combine like terms: 16.32653061 + -16.32653061 = 0.00000000 0.00000000 + -27.95918367t + t2 = 0 + -16.32653061 -27.95918367t + t2 = 0 + -16.32653061 Combine like terms: 0 + -16.32653061 = -16.32653061 -27.95918367t + t2 = -16.32653061 The t term is -27.95918367t. Take half its coefficient (-13.97959184). Square it (195.4289880) and add it to both sides. Add '195.4289880' to each side of the equation. -27.95918367t + 195.4289880 + t2 = -16.32653061 + 195.4289880 Reorder the terms: 195.4289880 + -27.95918367t + t2 = -16.32653061 + 195.4289880 Combine like terms: -16.32653061 + 195.4289880 = 179.10245739 195.4289880 + -27.95918367t + t2 = 179.10245739 Factor a perfect square on the left side: (t + -13.97959184)(t + -13.97959184) = 179.10245739 Calculate the square root of the right side: 13.382916625 Break this problem into two subproblems by setting (t + -13.97959184) equal to 13.382916625 and -13.382916625.Subproblem 1
t + -13.97959184 = 13.382916625 Simplifying t + -13.97959184 = 13.382916625 Reorder the terms: -13.97959184 + t = 13.382916625 Solving -13.97959184 + t = 13.382916625 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.97959184' to each side of the equation. -13.97959184 + 13.97959184 + t = 13.382916625 + 13.97959184 Combine like terms: -13.97959184 + 13.97959184 = 0.00000000 0.00000000 + t = 13.382916625 + 13.97959184 t = 13.382916625 + 13.97959184 Combine like terms: 13.382916625 + 13.97959184 = 27.362508465 t = 27.362508465 Simplifying t = 27.362508465Subproblem 2
t + -13.97959184 = -13.382916625 Simplifying t + -13.97959184 = -13.382916625 Reorder the terms: -13.97959184 + t = -13.382916625 Solving -13.97959184 + t = -13.382916625 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.97959184' to each side of the equation. -13.97959184 + 13.97959184 + t = -13.382916625 + 13.97959184 Combine like terms: -13.97959184 + 13.97959184 = 0.00000000 0.00000000 + t = -13.382916625 + 13.97959184 t = -13.382916625 + 13.97959184 Combine like terms: -13.382916625 + 13.97959184 = 0.596675215 t = 0.596675215 Simplifying t = 0.596675215Solution
The solution to the problem is based on the solutions from the subproblems. t = {27.362508465, 0.596675215}
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