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Simplifying 310 = -16t2 + 230t Reorder the terms: 310 = 230t + -16t2 Solving 310 = 230t + -16t2 Solving for variable 't'. Reorder the terms: 310 + -230t + 16t2 = 230t + -230t + -16t2 + 16t2 Combine like terms: 230t + -230t = 0 310 + -230t + 16t2 = 0 + -16t2 + 16t2 310 + -230t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 310 + -230t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(155 + -115t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(155 + -115t + 8t2)' equal to zero and attempt to solve: Simplifying 155 + -115t + 8t2 = 0 Solving 155 + -115t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 19.375 + -14.375t + t2 = 0 Move the constant term to the right: Add '-19.375' to each side of the equation. 19.375 + -14.375t + -19.375 + t2 = 0 + -19.375 Reorder the terms: 19.375 + -19.375 + -14.375t + t2 = 0 + -19.375 Combine like terms: 19.375 + -19.375 = 0.000 0.000 + -14.375t + t2 = 0 + -19.375 -14.375t + t2 = 0 + -19.375 Combine like terms: 0 + -19.375 = -19.375 -14.375t + t2 = -19.375 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 = -19.375 + 51.66015625 Reorder the terms: 51.66015625 + -14.375t + t2 = -19.375 + 51.66015625 Combine like terms: -19.375 + 51.66015625 = 32.28515625 51.66015625 + -14.375t + t2 = 32.28515625 Factor a perfect square on the left side: (t + -7.1875)(t + -7.1875) = 32.28515625 Calculate the square root of the right side: 5.682002838 Break this problem into two subproblems by setting (t + -7.1875) equal to 5.682002838 and -5.682002838.Subproblem 1
t + -7.1875 = 5.682002838 Simplifying t + -7.1875 = 5.682002838 Reorder the terms: -7.1875 + t = 5.682002838 Solving -7.1875 + t = 5.682002838 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 = 5.682002838 + 7.1875 Combine like terms: -7.1875 + 7.1875 = 0.0000 0.0000 + t = 5.682002838 + 7.1875 t = 5.682002838 + 7.1875 Combine like terms: 5.682002838 + 7.1875 = 12.869502838 t = 12.869502838 Simplifying t = 12.869502838Subproblem 2
t + -7.1875 = -5.682002838 Simplifying t + -7.1875 = -5.682002838 Reorder the terms: -7.1875 + t = -5.682002838 Solving -7.1875 + t = -5.682002838 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 = -5.682002838 + 7.1875 Combine like terms: -7.1875 + 7.1875 = 0.0000 0.0000 + t = -5.682002838 + 7.1875 t = -5.682002838 + 7.1875 Combine like terms: -5.682002838 + 7.1875 = 1.505497162 t = 1.505497162 Simplifying t = 1.505497162Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.869502838, 1.505497162}Solution
t = {12.869502838, 1.505497162}
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