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Simplifying 15 = -16t2 + -44t Reorder the terms: 15 = -44t + -16t2 Solving 15 = -44t + -16t2 Solving for variable 't'. Reorder the terms: 15 + 44t + 16t2 = -44t + 44t + -16t2 + 16t2 Combine like terms: -44t + 44t = 0 15 + 44t + 16t2 = 0 + -16t2 + 16t2 15 + 44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 15 + 44t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.9375 + 2.75t + t2 = 0 Move the constant term to the right: Add '-0.9375' to each side of the equation. 0.9375 + 2.75t + -0.9375 + t2 = 0 + -0.9375 Reorder the terms: 0.9375 + -0.9375 + 2.75t + t2 = 0 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + 2.75t + t2 = 0 + -0.9375 2.75t + t2 = 0 + -0.9375 Combine like terms: 0 + -0.9375 = -0.9375 2.75t + t2 = -0.9375 The t term is 2.75t. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75t + 1.890625 + t2 = -0.9375 + 1.890625 Reorder the terms: 1.890625 + 2.75t + t2 = -0.9375 + 1.890625 Combine like terms: -0.9375 + 1.890625 = 0.953125 1.890625 + 2.75t + t2 = 0.953125 Factor a perfect square on the left side: (t + 1.375)(t + 1.375) = 0.953125 Calculate the square root of the right side: 0.976281209 Break this problem into two subproblems by setting (t + 1.375) equal to 0.976281209 and -0.976281209.Subproblem 1
t + 1.375 = 0.976281209 Simplifying t + 1.375 = 0.976281209 Reorder the terms: 1.375 + t = 0.976281209 Solving 1.375 + t = 0.976281209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = 0.976281209 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = 0.976281209 + -1.375 t = 0.976281209 + -1.375 Combine like terms: 0.976281209 + -1.375 = -0.398718791 t = -0.398718791 Simplifying t = -0.398718791Subproblem 2
t + 1.375 = -0.976281209 Simplifying t + 1.375 = -0.976281209 Reorder the terms: 1.375 + t = -0.976281209 Solving 1.375 + t = -0.976281209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = -0.976281209 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = -0.976281209 + -1.375 t = -0.976281209 + -1.375 Combine like terms: -0.976281209 + -1.375 = -2.351281209 t = -2.351281209 Simplifying t = -2.351281209Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.398718791, -2.351281209}
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