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Simplifying 4.9(t2) + -11t + -85 = 0 Reorder the terms: -85 + -11t + 4.9t2 = 0 Solving -85 + -11t + 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'. -17.34693878 + -2.244897959t + t2 = 0 Move the constant term to the right: Add '17.34693878' to each side of the equation. -17.34693878 + -2.244897959t + 17.34693878 + t2 = 0 + 17.34693878 Reorder the terms: -17.34693878 + 17.34693878 + -2.244897959t + t2 = 0 + 17.34693878 Combine like terms: -17.34693878 + 17.34693878 = 0.00000000 0.00000000 + -2.244897959t + t2 = 0 + 17.34693878 -2.244897959t + t2 = 0 + 17.34693878 Combine like terms: 0 + 17.34693878 = 17.34693878 -2.244897959t + t2 = 17.34693878 The t term is -2.244897959t. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959t + 1.259891713 + t2 = 17.34693878 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959t + t2 = 17.34693878 + 1.259891713 Combine like terms: 17.34693878 + 1.259891713 = 18.606830493 1.259891713 + -2.244897959t + t2 = 18.606830493 Factor a perfect square on the left side: (t + -1.12244898)(t + -1.12244898) = 18.606830493 Calculate the square root of the right side: 4.313563549 Break this problem into two subproblems by setting (t + -1.12244898) equal to 4.313563549 and -4.313563549.Subproblem 1
t + -1.12244898 = 4.313563549 Simplifying t + -1.12244898 = 4.313563549 Reorder the terms: -1.12244898 + t = 4.313563549 Solving -1.12244898 + t = 4.313563549 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = 4.313563549 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = 4.313563549 + 1.12244898 t = 4.313563549 + 1.12244898 Combine like terms: 4.313563549 + 1.12244898 = 5.436012529 t = 5.436012529 Simplifying t = 5.436012529Subproblem 2
t + -1.12244898 = -4.313563549 Simplifying t + -1.12244898 = -4.313563549 Reorder the terms: -1.12244898 + t = -4.313563549 Solving -1.12244898 + t = -4.313563549 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = -4.313563549 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = -4.313563549 + 1.12244898 t = -4.313563549 + 1.12244898 Combine like terms: -4.313563549 + 1.12244898 = -3.191114569 t = -3.191114569 Simplifying t = -3.191114569Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.436012529, -3.191114569}
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