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Simplifying 0 = -16t2 + -4t + 382 Reorder the terms: 0 = 382 + -4t + -16t2 Solving 0 = 382 + -4t + -16t2 Solving for variable 't'. Combine like terms: 0 + -382 = -382 -382 + 4t + 16t2 = 382 + -4t + -16t2 + -382 + 4t + 16t2 Reorder the terms: -382 + 4t + 16t2 = 382 + -382 + -4t + 4t + -16t2 + 16t2 Combine like terms: 382 + -382 = 0 -382 + 4t + 16t2 = 0 + -4t + 4t + -16t2 + 16t2 -382 + 4t + 16t2 = -4t + 4t + -16t2 + 16t2 Combine like terms: -4t + 4t = 0 -382 + 4t + 16t2 = 0 + -16t2 + 16t2 -382 + 4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -382 + 4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-191 + 2t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-191 + 2t + 8t2)' equal to zero and attempt to solve: Simplifying -191 + 2t + 8t2 = 0 Solving -191 + 2t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -23.875 + 0.25t + t2 = 0 Move the constant term to the right: Add '23.875' to each side of the equation. -23.875 + 0.25t + 23.875 + t2 = 0 + 23.875 Reorder the terms: -23.875 + 23.875 + 0.25t + t2 = 0 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + 0.25t + t2 = 0 + 23.875 0.25t + t2 = 0 + 23.875 Combine like terms: 0 + 23.875 = 23.875 0.25t + t2 = 23.875 The t term is 0.25t. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25t + 0.015625 + t2 = 23.875 + 0.015625 Reorder the terms: 0.015625 + 0.25t + t2 = 23.875 + 0.015625 Combine like terms: 23.875 + 0.015625 = 23.890625 0.015625 + 0.25t + t2 = 23.890625 Factor a perfect square on the left side: (t + 0.125)(t + 0.125) = 23.890625 Calculate the square root of the right side: 4.887803699 Break this problem into two subproblems by setting (t + 0.125) equal to 4.887803699 and -4.887803699.Subproblem 1
t + 0.125 = 4.887803699 Simplifying t + 0.125 = 4.887803699 Reorder the terms: 0.125 + t = 4.887803699 Solving 0.125 + t = 4.887803699 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = 4.887803699 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = 4.887803699 + -0.125 t = 4.887803699 + -0.125 Combine like terms: 4.887803699 + -0.125 = 4.762803699 t = 4.762803699 Simplifying t = 4.762803699Subproblem 2
t + 0.125 = -4.887803699 Simplifying t + 0.125 = -4.887803699 Reorder the terms: 0.125 + t = -4.887803699 Solving 0.125 + t = -4.887803699 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = -4.887803699 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = -4.887803699 + -0.125 t = -4.887803699 + -0.125 Combine like terms: -4.887803699 + -0.125 = -5.012803699 t = -5.012803699 Simplifying t = -5.012803699Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.762803699, -5.012803699}Solution
t = {4.762803699, -5.012803699}
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