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Simplifying 0 = -0.16t2 + 5t + -17 Reorder the terms: 0 = -17 + 5t + -0.16t2 Solving 0 = -17 + 5t + -0.16t2 Solving for variable 't'. Combine like terms: 0 + 17 = 17 17 + -5t + 0.16t2 = -17 + 5t + -0.16t2 + 17 + -5t + 0.16t2 Reorder the terms: 17 + -5t + 0.16t2 = -17 + 17 + 5t + -5t + -0.16t2 + 0.16t2 Combine like terms: -17 + 17 = 0 17 + -5t + 0.16t2 = 0 + 5t + -5t + -0.16t2 + 0.16t2 17 + -5t + 0.16t2 = 5t + -5t + -0.16t2 + 0.16t2 Combine like terms: 5t + -5t = 0 17 + -5t + 0.16t2 = 0 + -0.16t2 + 0.16t2 17 + -5t + 0.16t2 = -0.16t2 + 0.16t2 Combine like terms: -0.16t2 + 0.16t2 = 0.00 17 + -5t + 0.16t2 = 0.00 Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. 106.25 + -31.25t + t2 = 0 Move the constant term to the right: Add '-106.25' to each side of the equation. 106.25 + -31.25t + -106.25 + t2 = 0 + -106.25 Reorder the terms: 106.25 + -106.25 + -31.25t + t2 = 0 + -106.25 Combine like terms: 106.25 + -106.25 = 0.00 0.00 + -31.25t + t2 = 0 + -106.25 -31.25t + t2 = 0 + -106.25 Combine like terms: 0 + -106.25 = -106.25 -31.25t + t2 = -106.25 The t term is -31.25t. Take half its coefficient (-15.625). Square it (244.140625) and add it to both sides. Add '244.140625' to each side of the equation. -31.25t + 244.140625 + t2 = -106.25 + 244.140625 Reorder the terms: 244.140625 + -31.25t + t2 = -106.25 + 244.140625 Combine like terms: -106.25 + 244.140625 = 137.890625 244.140625 + -31.25t + t2 = 137.890625 Factor a perfect square on the left side: (t + -15.625)(t + -15.625) = 137.890625 Calculate the square root of the right side: 11.742683893 Break this problem into two subproblems by setting (t + -15.625) equal to 11.742683893 and -11.742683893.Subproblem 1
t + -15.625 = 11.742683893 Simplifying t + -15.625 = 11.742683893 Reorder the terms: -15.625 + t = 11.742683893 Solving -15.625 + t = 11.742683893 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + t = 11.742683893 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + t = 11.742683893 + 15.625 t = 11.742683893 + 15.625 Combine like terms: 11.742683893 + 15.625 = 27.367683893 t = 27.367683893 Simplifying t = 27.367683893Subproblem 2
t + -15.625 = -11.742683893 Simplifying t + -15.625 = -11.742683893 Reorder the terms: -15.625 + t = -11.742683893 Solving -15.625 + t = -11.742683893 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + t = -11.742683893 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + t = -11.742683893 + 15.625 t = -11.742683893 + 15.625 Combine like terms: -11.742683893 + 15.625 = 3.882316107 t = 3.882316107 Simplifying t = 3.882316107Solution
The solution to the problem is based on the solutions from the subproblems. t = {27.367683893, 3.882316107}
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