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Simplifying 0 = 16t2 + 30t + -1 Reorder the terms: 0 = -1 + 30t + 16t2 Solving 0 = -1 + 30t + 16t2 Solving for variable 't'. Combine like terms: 0 + 1 = 1 1 + -30t + -16t2 = -1 + 30t + 16t2 + 1 + -30t + -16t2 Reorder the terms: 1 + -30t + -16t2 = -1 + 1 + 30t + -30t + 16t2 + -16t2 Combine like terms: -1 + 1 = 0 1 + -30t + -16t2 = 0 + 30t + -30t + 16t2 + -16t2 1 + -30t + -16t2 = 30t + -30t + 16t2 + -16t2 Combine like terms: 30t + -30t = 0 1 + -30t + -16t2 = 0 + 16t2 + -16t2 1 + -30t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 1 + -30t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.0625 + 1.875t + t2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 1.875t + 0.0625 + t2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 1.875t + t2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 1.875t + t2 = 0 + 0.0625 1.875t + t2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 1.875t + t2 = 0.0625 The t term is 1.875t. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875t + 0.87890625 + t2 = 0.0625 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 0.0625 + 0.87890625 Combine like terms: 0.0625 + 0.87890625 = 0.94140625 0.87890625 + 1.875t + t2 = 0.94140625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (t + 0.9375) equal to 0.970260919 and -0.970260919.Subproblem 1
t + 0.9375 = 0.970260919 Simplifying t + 0.9375 = 0.970260919 Reorder the terms: 0.9375 + t = 0.970260919 Solving 0.9375 + t = 0.970260919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = 0.970260919 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 0.970260919 + -0.9375 t = 0.970260919 + -0.9375 Combine like terms: 0.970260919 + -0.9375 = 0.032760919 t = 0.032760919 Simplifying t = 0.032760919Subproblem 2
t + 0.9375 = -0.970260919 Simplifying t + 0.9375 = -0.970260919 Reorder the terms: 0.9375 + t = -0.970260919 Solving 0.9375 + t = -0.970260919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = -0.970260919 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -0.970260919 + -0.9375 t = -0.970260919 + -0.9375 Combine like terms: -0.970260919 + -0.9375 = -1.907760919 t = -1.907760919 Simplifying t = -1.907760919Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.032760919, -1.907760919}
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