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Simplifying 6 = (-16t2) + (30t) + 5 Reorder the terms: 6 = 5 + (30t) + (-16t2) Solving 6 = 5 + (30t) + (-16t2) Solving for variable 't'. Combine like terms: 6 + -5 = 1 1 + (-30t) + (16t2) = 5 + (30t) + (-16t2) + -5 + (-30t) + (16t2) Reorder the terms: 1 + (-30t) + (16t2) = 5 + -5 + (30t) + (-30t) + (-16t2) + (16t2) Combine like terms: 5 + -5 = 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 = 0.81640625 0.87890625 + (-1.875t) + t2 = 0.81640625 Factor a perfect square on the left side: ((t) + -0.9375)((t) + -0.9375) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting ((t) + -0.9375) equal to 0.903552018 and -0.903552018.Subproblem 1
(t) + -0.9375 = 0.903552018 Simplifying (t) + -0.9375 = 0.903552018 t + -0.9375 = 0.903552018 Reorder the terms: -0.9375 + t = 0.903552018 Solving -0.9375 + t = 0.903552018 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 = 0.903552018 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 0.903552018 + 0.9375 t = 0.903552018 + 0.9375 Combine like terms: 0.903552018 + 0.9375 = 1.841052018 t = 1.841052018 Simplifying t = 1.841052018Subproblem 2
(t) + -0.9375 = -0.903552018 Simplifying (t) + -0.9375 = -0.903552018 t + -0.9375 = -0.903552018 Reorder the terms: -0.9375 + t = -0.903552018 Solving -0.9375 + t = -0.903552018 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 = -0.903552018 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -0.903552018 + 0.9375 t = -0.903552018 + 0.9375 Combine like terms: -0.903552018 + 0.9375 = 0.033947982 t = 0.033947982 Simplifying t = 0.033947982Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.841052018, 0.033947982}
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