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Simplifying 15.1 = -16t2 + 30t + 6 Reorder the terms: 15.1 = 6 + 30t + -16t2 Solving 15.1 = 6 + 30t + -16t2 Solving for variable 't'. Combine like terms: 15.1 + -6 = 9.1 9.1 + -30t + 16t2 = 6 + 30t + -16t2 + -6 + -30t + 16t2 Reorder the terms: 9.1 + -30t + 16t2 = 6 + -6 + 30t + -30t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 9.1 + -30t + 16t2 = 0 + 30t + -30t + -16t2 + 16t2 9.1 + -30t + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 9.1 + -30t + 16t2 = 0 + -16t2 + 16t2 9.1 + -30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 9.1 + -30t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.56875 + -1.875t + t2 = 0 Move the constant term to the right: Add '-0.56875' to each side of the equation. 0.56875 + -1.875t + -0.56875 + t2 = 0 + -0.56875 Reorder the terms: 0.56875 + -0.56875 + -1.875t + t2 = 0 + -0.56875 Combine like terms: 0.56875 + -0.56875 = 0.00000 0.00000 + -1.875t + t2 = 0 + -0.56875 -1.875t + t2 = 0 + -0.56875 Combine like terms: 0 + -0.56875 = -0.56875 -1.875t + t2 = -0.56875 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 = -0.56875 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = -0.56875 + 0.87890625 Combine like terms: -0.56875 + 0.87890625 = 0.31015625 0.87890625 + -1.875t + t2 = 0.31015625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 0.31015625 Calculate the square root of the right side: 0.556916735 Break this problem into two subproblems by setting (t + -0.9375) equal to 0.556916735 and -0.556916735.Subproblem 1
t + -0.9375 = 0.556916735 Simplifying t + -0.9375 = 0.556916735 Reorder the terms: -0.9375 + t = 0.556916735 Solving -0.9375 + t = 0.556916735 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 = 0.556916735 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 0.556916735 + 0.9375 t = 0.556916735 + 0.9375 Combine like terms: 0.556916735 + 0.9375 = 1.494416735 t = 1.494416735 Simplifying t = 1.494416735Subproblem 2
t + -0.9375 = -0.556916735 Simplifying t + -0.9375 = -0.556916735 Reorder the terms: -0.9375 + t = -0.556916735 Solving -0.9375 + t = -0.556916735 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 = -0.556916735 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -0.556916735 + 0.9375 t = -0.556916735 + 0.9375 Combine like terms: -0.556916735 + 0.9375 = 0.380583265 t = 0.380583265 Simplifying t = 0.380583265Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.494416735, 0.380583265}
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