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Simplifying 16 = 3 + 30t + -16t2 Solving 16 = 3 + 30t + -16t2 Solving for variable 't'. Combine like terms: 16 + -3 = 13 13 + -30t + 16t2 = 3 + 30t + -16t2 + -3 + -30t + 16t2 Reorder the terms: 13 + -30t + 16t2 = 3 + -3 + 30t + -30t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 13 + -30t + 16t2 = 0 + 30t + -30t + -16t2 + 16t2 13 + -30t + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 13 + -30t + 16t2 = 0 + -16t2 + 16t2 13 + -30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 13 + -30t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.8125 + -1.875t + t2 = 0 Move the constant term to the right: Add '-0.8125' to each side of the equation. 0.8125 + -1.875t + -0.8125 + t2 = 0 + -0.8125 Reorder the terms: 0.8125 + -0.8125 + -1.875t + t2 = 0 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + -1.875t + t2 = 0 + -0.8125 -1.875t + t2 = 0 + -0.8125 Combine like terms: 0 + -0.8125 = -0.8125 -1.875t + t2 = -0.8125 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 = -0.8125 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = -0.8125 + 0.87890625 Combine like terms: -0.8125 + 0.87890625 = 0.06640625 0.87890625 + -1.875t + t2 = 0.06640625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (t + -0.9375) equal to 0.257694102 and -0.257694102.Subproblem 1
t + -0.9375 = 0.257694102 Simplifying t + -0.9375 = 0.257694102 Reorder the terms: -0.9375 + t = 0.257694102 Solving -0.9375 + t = 0.257694102 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 = 0.257694102 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 0.257694102 + 0.9375 t = 0.257694102 + 0.9375 Combine like terms: 0.257694102 + 0.9375 = 1.195194102 t = 1.195194102 Simplifying t = 1.195194102Subproblem 2
t + -0.9375 = -0.257694102 Simplifying t + -0.9375 = -0.257694102 Reorder the terms: -0.9375 + t = -0.257694102 Solving -0.9375 + t = -0.257694102 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 = -0.257694102 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -0.257694102 + 0.9375 t = -0.257694102 + 0.9375 Combine like terms: -0.257694102 + 0.9375 = 0.679805898 t = 0.679805898 Simplifying t = 0.679805898Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.195194102, 0.679805898}
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