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Simplifying 85 = 175t + 16t2 Solving 85 = 175t + 16t2 Solving for variable 't'. Reorder the terms: 85 + -175t + -16t2 = 175t + -175t + 16t2 + -16t2 Combine like terms: 175t + -175t = 0 85 + -175t + -16t2 = 0 + 16t2 + -16t2 85 + -175t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 85 + -175t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -5.3125 + 10.9375t + t2 = 0 Move the constant term to the right: Add '5.3125' to each side of the equation. -5.3125 + 10.9375t + 5.3125 + t2 = 0 + 5.3125 Reorder the terms: -5.3125 + 5.3125 + 10.9375t + t2 = 0 + 5.3125 Combine like terms: -5.3125 + 5.3125 = 0.0000 0.0000 + 10.9375t + t2 = 0 + 5.3125 10.9375t + t2 = 0 + 5.3125 Combine like terms: 0 + 5.3125 = 5.3125 10.9375t + t2 = 5.3125 The t term is 10.9375t. Take half its coefficient (5.46875). Square it (29.90722656) and add it to both sides. Add '29.90722656' to each side of the equation. 10.9375t + 29.90722656 + t2 = 5.3125 + 29.90722656 Reorder the terms: 29.90722656 + 10.9375t + t2 = 5.3125 + 29.90722656 Combine like terms: 5.3125 + 29.90722656 = 35.21972656 29.90722656 + 10.9375t + t2 = 35.21972656 Factor a perfect square on the left side: (t + 5.46875)(t + 5.46875) = 35.21972656 Calculate the square root of the right side: 5.934621012 Break this problem into two subproblems by setting (t + 5.46875) equal to 5.934621012 and -5.934621012.Subproblem 1
t + 5.46875 = 5.934621012 Simplifying t + 5.46875 = 5.934621012 Reorder the terms: 5.46875 + t = 5.934621012 Solving 5.46875 + t = 5.934621012 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.46875' to each side of the equation. 5.46875 + -5.46875 + t = 5.934621012 + -5.46875 Combine like terms: 5.46875 + -5.46875 = 0.00000 0.00000 + t = 5.934621012 + -5.46875 t = 5.934621012 + -5.46875 Combine like terms: 5.934621012 + -5.46875 = 0.465871012 t = 0.465871012 Simplifying t = 0.465871012Subproblem 2
t + 5.46875 = -5.934621012 Simplifying t + 5.46875 = -5.934621012 Reorder the terms: 5.46875 + t = -5.934621012 Solving 5.46875 + t = -5.934621012 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.46875' to each side of the equation. 5.46875 + -5.46875 + t = -5.934621012 + -5.46875 Combine like terms: 5.46875 + -5.46875 = 0.00000 0.00000 + t = -5.934621012 + -5.46875 t = -5.934621012 + -5.46875 Combine like terms: -5.934621012 + -5.46875 = -11.403371012 t = -11.403371012 Simplifying t = -11.403371012Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.465871012, -11.403371012}
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