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Simplifying 0.0885t2 + -0.922t + 1.745 = 0 Reorder the terms: 1.745 + -0.922t + 0.0885t2 = 0 Solving 1.745 + -0.922t + 0.0885t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0885 the coefficient of the squared term: Divide each side by '0.0885'. 19.71751412 + -10.4180791t + t2 = 0 Move the constant term to the right: Add '-19.71751412' to each side of the equation. 19.71751412 + -10.4180791t + -19.71751412 + t2 = 0 + -19.71751412 Reorder the terms: 19.71751412 + -19.71751412 + -10.4180791t + t2 = 0 + -19.71751412 Combine like terms: 19.71751412 + -19.71751412 = 0.00000000 0.00000000 + -10.4180791t + t2 = 0 + -19.71751412 -10.4180791t + t2 = 0 + -19.71751412 Combine like terms: 0 + -19.71751412 = -19.71751412 -10.4180791t + t2 = -19.71751412 The t term is -10.4180791t. Take half its coefficient (-5.20903955). Square it (27.13409303) and add it to both sides. Add '27.13409303' to each side of the equation. -10.4180791t + 27.13409303 + t2 = -19.71751412 + 27.13409303 Reorder the terms: 27.13409303 + -10.4180791t + t2 = -19.71751412 + 27.13409303 Combine like terms: -19.71751412 + 27.13409303 = 7.41657891 27.13409303 + -10.4180791t + t2 = 7.41657891 Factor a perfect square on the left side: (t + -5.20903955)(t + -5.20903955) = 7.41657891 Calculate the square root of the right side: 2.723339661 Break this problem into two subproblems by setting (t + -5.20903955) equal to 2.723339661 and -2.723339661.Subproblem 1
t + -5.20903955 = 2.723339661 Simplifying t + -5.20903955 = 2.723339661 Reorder the terms: -5.20903955 + t = 2.723339661 Solving -5.20903955 + t = 2.723339661 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.20903955' to each side of the equation. -5.20903955 + 5.20903955 + t = 2.723339661 + 5.20903955 Combine like terms: -5.20903955 + 5.20903955 = 0.00000000 0.00000000 + t = 2.723339661 + 5.20903955 t = 2.723339661 + 5.20903955 Combine like terms: 2.723339661 + 5.20903955 = 7.932379211 t = 7.932379211 Simplifying t = 7.932379211Subproblem 2
t + -5.20903955 = -2.723339661 Simplifying t + -5.20903955 = -2.723339661 Reorder the terms: -5.20903955 + t = -2.723339661 Solving -5.20903955 + t = -2.723339661 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.20903955' to each side of the equation. -5.20903955 + 5.20903955 + t = -2.723339661 + 5.20903955 Combine like terms: -5.20903955 + 5.20903955 = 0.00000000 0.00000000 + t = -2.723339661 + 5.20903955 t = -2.723339661 + 5.20903955 Combine like terms: -2.723339661 + 5.20903955 = 2.485699889 t = 2.485699889 Simplifying t = 2.485699889Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.932379211, 2.485699889}
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