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Simplifying 126.9t = 160 + 92t + -16t2 Solving 126.9t = 160 + 92t + -16t2 Solving for variable 't'. Reorder the terms: -160 + 126.9t + -92t + 16t2 = 160 + 92t + -16t2 + -160 + -92t + 16t2 Combine like terms: 126.9t + -92t = 34.9t -160 + 34.9t + 16t2 = 160 + 92t + -16t2 + -160 + -92t + 16t2 Reorder the terms: -160 + 34.9t + 16t2 = 160 + -160 + 92t + -92t + -16t2 + 16t2 Combine like terms: 160 + -160 = 0 -160 + 34.9t + 16t2 = 0 + 92t + -92t + -16t2 + 16t2 -160 + 34.9t + 16t2 = 92t + -92t + -16t2 + 16t2 Combine like terms: 92t + -92t = 0 -160 + 34.9t + 16t2 = 0 + -16t2 + 16t2 -160 + 34.9t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -160 + 34.9t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10 + 2.18125t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 2.18125t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + 2.18125t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2.18125t + t2 = 0 + 10 2.18125t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 2.18125t + t2 = 10 The t term is 2.18125t. Take half its coefficient (1.090625). Square it (1.189462891) and add it to both sides. Add '1.189462891' to each side of the equation. 2.18125t + 1.189462891 + t2 = 10 + 1.189462891 Reorder the terms: 1.189462891 + 2.18125t + t2 = 10 + 1.189462891 Combine like terms: 10 + 1.189462891 = 11.189462891 1.189462891 + 2.18125t + t2 = 11.189462891 Factor a perfect square on the left side: (t + 1.090625)(t + 1.090625) = 11.189462891 Calculate the square root of the right side: 3.345065454 Break this problem into two subproblems by setting (t + 1.090625) equal to 3.345065454 and -3.345065454.Subproblem 1
t + 1.090625 = 3.345065454 Simplifying t + 1.090625 = 3.345065454 Reorder the terms: 1.090625 + t = 3.345065454 Solving 1.090625 + t = 3.345065454 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.090625' to each side of the equation. 1.090625 + -1.090625 + t = 3.345065454 + -1.090625 Combine like terms: 1.090625 + -1.090625 = 0.000000 0.000000 + t = 3.345065454 + -1.090625 t = 3.345065454 + -1.090625 Combine like terms: 3.345065454 + -1.090625 = 2.254440454 t = 2.254440454 Simplifying t = 2.254440454Subproblem 2
t + 1.090625 = -3.345065454 Simplifying t + 1.090625 = -3.345065454 Reorder the terms: 1.090625 + t = -3.345065454 Solving 1.090625 + t = -3.345065454 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.090625' to each side of the equation. 1.090625 + -1.090625 + t = -3.345065454 + -1.090625 Combine like terms: 1.090625 + -1.090625 = 0.000000 0.000000 + t = -3.345065454 + -1.090625 t = -3.345065454 + -1.090625 Combine like terms: -3.345065454 + -1.090625 = -4.435690454 t = -4.435690454 Simplifying t = -4.435690454Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.254440454, -4.435690454}
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