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Simplifying 110 = 230t + -16t2 Solving 110 = 230t + -16t2 Solving for variable 't'. Reorder the terms: 110 + -230t + 16t2 = 230t + -230t + -16t2 + 16t2 Combine like terms: 230t + -230t = 0 110 + -230t + 16t2 = 0 + -16t2 + 16t2 110 + -230t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 110 + -230t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(55 + -115t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + -115t + 8t2)' equal to zero and attempt to solve: Simplifying 55 + -115t + 8t2 = 0 Solving 55 + -115t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.875 + -14.375t + t2 = 0 Move the constant term to the right: Add '-6.875' to each side of the equation. 6.875 + -14.375t + -6.875 + t2 = 0 + -6.875 Reorder the terms: 6.875 + -6.875 + -14.375t + t2 = 0 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + -14.375t + t2 = 0 + -6.875 -14.375t + t2 = 0 + -6.875 Combine like terms: 0 + -6.875 = -6.875 -14.375t + t2 = -6.875 The t term is -14.375t. Take half its coefficient (-7.1875). Square it (51.66015625) and add it to both sides. Add '51.66015625' to each side of the equation. -14.375t + 51.66015625 + t2 = -6.875 + 51.66015625 Reorder the terms: 51.66015625 + -14.375t + t2 = -6.875 + 51.66015625 Combine like terms: -6.875 + 51.66015625 = 44.78515625 51.66015625 + -14.375t + t2 = 44.78515625 Factor a perfect square on the left side: (t + -7.1875)(t + -7.1875) = 44.78515625 Calculate the square root of the right side: 6.692171266 Break this problem into two subproblems by setting (t + -7.1875) equal to 6.692171266 and -6.692171266.Subproblem 1
t + -7.1875 = 6.692171266 Simplifying t + -7.1875 = 6.692171266 Reorder the terms: -7.1875 + t = 6.692171266 Solving -7.1875 + t = 6.692171266 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.1875' to each side of the equation. -7.1875 + 7.1875 + t = 6.692171266 + 7.1875 Combine like terms: -7.1875 + 7.1875 = 0.0000 0.0000 + t = 6.692171266 + 7.1875 t = 6.692171266 + 7.1875 Combine like terms: 6.692171266 + 7.1875 = 13.879671266 t = 13.879671266 Simplifying t = 13.879671266Subproblem 2
t + -7.1875 = -6.692171266 Simplifying t + -7.1875 = -6.692171266 Reorder the terms: -7.1875 + t = -6.692171266 Solving -7.1875 + t = -6.692171266 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.1875' to each side of the equation. -7.1875 + 7.1875 + t = -6.692171266 + 7.1875 Combine like terms: -7.1875 + 7.1875 = 0.0000 0.0000 + t = -6.692171266 + 7.1875 t = -6.692171266 + 7.1875 Combine like terms: -6.692171266 + 7.1875 = 0.495328734 t = 0.495328734 Simplifying t = 0.495328734Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.879671266, 0.495328734}Solution
t = {13.879671266, 0.495328734}
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