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Simplifying 0 = -16t2 + -38t + 1500 Reorder the terms: 0 = 1500 + -38t + -16t2 Solving 0 = 1500 + -38t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1500 = -1500 -1500 + 38t + 16t2 = 1500 + -38t + -16t2 + -1500 + 38t + 16t2 Reorder the terms: -1500 + 38t + 16t2 = 1500 + -1500 + -38t + 38t + -16t2 + 16t2 Combine like terms: 1500 + -1500 = 0 -1500 + 38t + 16t2 = 0 + -38t + 38t + -16t2 + 16t2 -1500 + 38t + 16t2 = -38t + 38t + -16t2 + 16t2 Combine like terms: -38t + 38t = 0 -1500 + 38t + 16t2 = 0 + -16t2 + 16t2 -1500 + 38t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1500 + 38t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-750 + 19t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-750 + 19t + 8t2)' equal to zero and attempt to solve: Simplifying -750 + 19t + 8t2 = 0 Solving -750 + 19t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -93.75 + 2.375t + t2 = 0 Move the constant term to the right: Add '93.75' to each side of the equation. -93.75 + 2.375t + 93.75 + t2 = 0 + 93.75 Reorder the terms: -93.75 + 93.75 + 2.375t + t2 = 0 + 93.75 Combine like terms: -93.75 + 93.75 = 0.00 0.00 + 2.375t + t2 = 0 + 93.75 2.375t + t2 = 0 + 93.75 Combine like terms: 0 + 93.75 = 93.75 2.375t + t2 = 93.75 The t term is 2.375t. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375t + 1.41015625 + t2 = 93.75 + 1.41015625 Reorder the terms: 1.41015625 + 2.375t + t2 = 93.75 + 1.41015625 Combine like terms: 93.75 + 1.41015625 = 95.16015625 1.41015625 + 2.375t + t2 = 95.16015625 Factor a perfect square on the left side: (t + 1.1875)(t + 1.1875) = 95.16015625 Calculate the square root of the right side: 9.755006727 Break this problem into two subproblems by setting (t + 1.1875) equal to 9.755006727 and -9.755006727.Subproblem 1
t + 1.1875 = 9.755006727 Simplifying t + 1.1875 = 9.755006727 Reorder the terms: 1.1875 + t = 9.755006727 Solving 1.1875 + t = 9.755006727 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + t = 9.755006727 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + t = 9.755006727 + -1.1875 t = 9.755006727 + -1.1875 Combine like terms: 9.755006727 + -1.1875 = 8.567506727 t = 8.567506727 Simplifying t = 8.567506727Subproblem 2
t + 1.1875 = -9.755006727 Simplifying t + 1.1875 = -9.755006727 Reorder the terms: 1.1875 + t = -9.755006727 Solving 1.1875 + t = -9.755006727 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + t = -9.755006727 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + t = -9.755006727 + -1.1875 t = -9.755006727 + -1.1875 Combine like terms: -9.755006727 + -1.1875 = -10.942506727 t = -10.942506727 Simplifying t = -10.942506727Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.567506727, -10.942506727}Solution
t = {8.567506727, -10.942506727}
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