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Simplifying 71 = 125t + -16t2 Solving 71 = 125t + -16t2 Solving for variable 't'. Reorder the terms: 71 + -125t + 16t2 = 125t + -125t + -16t2 + 16t2 Combine like terms: 125t + -125t = 0 71 + -125t + 16t2 = 0 + -16t2 + 16t2 71 + -125t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 71 + -125t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 4.4375 + -7.8125t + t2 = 0 Move the constant term to the right: Add '-4.4375' to each side of the equation. 4.4375 + -7.8125t + -4.4375 + t2 = 0 + -4.4375 Reorder the terms: 4.4375 + -4.4375 + -7.8125t + t2 = 0 + -4.4375 Combine like terms: 4.4375 + -4.4375 = 0.0000 0.0000 + -7.8125t + t2 = 0 + -4.4375 -7.8125t + t2 = 0 + -4.4375 Combine like terms: 0 + -4.4375 = -4.4375 -7.8125t + t2 = -4.4375 The t term is -7.8125t. Take half its coefficient (-3.90625). Square it (15.25878906) and add it to both sides. Add '15.25878906' to each side of the equation. -7.8125t + 15.25878906 + t2 = -4.4375 + 15.25878906 Reorder the terms: 15.25878906 + -7.8125t + t2 = -4.4375 + 15.25878906 Combine like terms: -4.4375 + 15.25878906 = 10.82128906 15.25878906 + -7.8125t + t2 = 10.82128906 Factor a perfect square on the left side: (t + -3.90625)(t + -3.90625) = 10.82128906 Calculate the square root of the right side: 3.289572778 Break this problem into two subproblems by setting (t + -3.90625) equal to 3.289572778 and -3.289572778.Subproblem 1
t + -3.90625 = 3.289572778 Simplifying t + -3.90625 = 3.289572778 Reorder the terms: -3.90625 + t = 3.289572778 Solving -3.90625 + t = 3.289572778 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + t = 3.289572778 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = 3.289572778 + 3.90625 t = 3.289572778 + 3.90625 Combine like terms: 3.289572778 + 3.90625 = 7.195822778 t = 7.195822778 Simplifying t = 7.195822778Subproblem 2
t + -3.90625 = -3.289572778 Simplifying t + -3.90625 = -3.289572778 Reorder the terms: -3.90625 + t = -3.289572778 Solving -3.90625 + t = -3.289572778 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + t = -3.289572778 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = -3.289572778 + 3.90625 t = -3.289572778 + 3.90625 Combine like terms: -3.289572778 + 3.90625 = 0.616677222 t = 0.616677222 Simplifying t = 0.616677222Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.195822778, 0.616677222}
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