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Simplifying 0 = -16t2 + 117t + 5 Reorder the terms: 0 = 5 + 117t + -16t2 Solving 0 = 5 + 117t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -117t + 16t2 = 5 + 117t + -16t2 + -5 + -117t + 16t2 Reorder the terms: -5 + -117t + 16t2 = 5 + -5 + 117t + -117t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + -117t + 16t2 = 0 + 117t + -117t + -16t2 + 16t2 -5 + -117t + 16t2 = 117t + -117t + -16t2 + 16t2 Combine like terms: 117t + -117t = 0 -5 + -117t + 16t2 = 0 + -16t2 + 16t2 -5 + -117t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -117t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -7.3125t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -7.3125t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -7.3125t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -7.3125t + t2 = 0 + 0.3125 -7.3125t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -7.3125t + t2 = 0.3125 The t term is -7.3125t. Take half its coefficient (-3.65625). Square it (13.36816406) and add it to both sides. Add '13.36816406' to each side of the equation. -7.3125t + 13.36816406 + t2 = 0.3125 + 13.36816406 Reorder the terms: 13.36816406 + -7.3125t + t2 = 0.3125 + 13.36816406 Combine like terms: 0.3125 + 13.36816406 = 13.68066406 13.36816406 + -7.3125t + t2 = 13.68066406 Factor a perfect square on the left side: (t + -3.65625)(t + -3.65625) = 13.68066406 Calculate the square root of the right side: 3.698738171 Break this problem into two subproblems by setting (t + -3.65625) equal to 3.698738171 and -3.698738171.Subproblem 1
t + -3.65625 = 3.698738171 Simplifying t + -3.65625 = 3.698738171 Reorder the terms: -3.65625 + t = 3.698738171 Solving -3.65625 + t = 3.698738171 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = 3.698738171 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = 3.698738171 + 3.65625 t = 3.698738171 + 3.65625 Combine like terms: 3.698738171 + 3.65625 = 7.354988171 t = 7.354988171 Simplifying t = 7.354988171Subproblem 2
t + -3.65625 = -3.698738171 Simplifying t + -3.65625 = -3.698738171 Reorder the terms: -3.65625 + t = -3.698738171 Solving -3.65625 + t = -3.698738171 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = -3.698738171 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = -3.698738171 + 3.65625 t = -3.698738171 + 3.65625 Combine like terms: -3.698738171 + 3.65625 = -0.042488171 t = -0.042488171 Simplifying t = -0.042488171Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.354988171, -0.042488171}
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