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Simplifying 16t2 + 85t + -50 = 0 Reorder the terms: -50 + 85t + 16t2 = 0 Solving -50 + 85t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.125 + 5.3125t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 5.3125t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 5.3125t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 5.3125t + t2 = 0 + 3.125 5.3125t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 5.3125t + t2 = 3.125 The t term is 5.3125t. Take half its coefficient (2.65625). Square it (7.055664063) and add it to both sides. Add '7.055664063' to each side of the equation. 5.3125t + 7.055664063 + t2 = 3.125 + 7.055664063 Reorder the terms: 7.055664063 + 5.3125t + t2 = 3.125 + 7.055664063 Combine like terms: 3.125 + 7.055664063 = 10.180664063 7.055664063 + 5.3125t + t2 = 10.180664063 Factor a perfect square on the left side: (t + 2.65625)(t + 2.65625) = 10.180664063 Calculate the square root of the right side: 3.19071529 Break this problem into two subproblems by setting (t + 2.65625) equal to 3.19071529 and -3.19071529.Subproblem 1
t + 2.65625 = 3.19071529 Simplifying t + 2.65625 = 3.19071529 Reorder the terms: 2.65625 + t = 3.19071529 Solving 2.65625 + t = 3.19071529 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.65625' to each side of the equation. 2.65625 + -2.65625 + t = 3.19071529 + -2.65625 Combine like terms: 2.65625 + -2.65625 = 0.00000 0.00000 + t = 3.19071529 + -2.65625 t = 3.19071529 + -2.65625 Combine like terms: 3.19071529 + -2.65625 = 0.53446529 t = 0.53446529 Simplifying t = 0.53446529Subproblem 2
t + 2.65625 = -3.19071529 Simplifying t + 2.65625 = -3.19071529 Reorder the terms: 2.65625 + t = -3.19071529 Solving 2.65625 + t = -3.19071529 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.65625' to each side of the equation. 2.65625 + -2.65625 + t = -3.19071529 + -2.65625 Combine like terms: 2.65625 + -2.65625 = 0.00000 0.00000 + t = -3.19071529 + -2.65625 t = -3.19071529 + -2.65625 Combine like terms: -3.19071529 + -2.65625 = -5.84696529 t = -5.84696529 Simplifying t = -5.84696529Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.53446529, -5.84696529}
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