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Simplifying 0 = -16t2 + 125t + 3 Reorder the terms: 0 = 3 + 125t + -16t2 Solving 0 = 3 + 125t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -125t + 16t2 = 3 + 125t + -16t2 + -3 + -125t + 16t2 Reorder the terms: -3 + -125t + 16t2 = 3 + -3 + 125t + -125t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -125t + 16t2 = 0 + 125t + -125t + -16t2 + 16t2 -3 + -125t + 16t2 = 125t + -125t + -16t2 + 16t2 Combine like terms: 125t + -125t = 0 -3 + -125t + 16t2 = 0 + -16t2 + 16t2 -3 + -125t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -125t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -7.8125t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -7.8125t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -7.8125t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -7.8125t + t2 = 0 + 0.1875 -7.8125t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -7.8125t + t2 = 0.1875 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 = 0.1875 + 15.25878906 Reorder the terms: 15.25878906 + -7.8125t + t2 = 0.1875 + 15.25878906 Combine like terms: 0.1875 + 15.25878906 = 15.44628906 15.25878906 + -7.8125t + t2 = 15.44628906 Factor a perfect square on the left side: (t + -3.90625)(t + -3.90625) = 15.44628906 Calculate the square root of the right side: 3.930176721 Break this problem into two subproblems by setting (t + -3.90625) equal to 3.930176721 and -3.930176721.Subproblem 1
t + -3.90625 = 3.930176721 Simplifying t + -3.90625 = 3.930176721 Reorder the terms: -3.90625 + t = 3.930176721 Solving -3.90625 + t = 3.930176721 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 = 3.930176721 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = 3.930176721 + 3.90625 t = 3.930176721 + 3.90625 Combine like terms: 3.930176721 + 3.90625 = 7.836426721 t = 7.836426721 Simplifying t = 7.836426721Subproblem 2
t + -3.90625 = -3.930176721 Simplifying t + -3.90625 = -3.930176721 Reorder the terms: -3.90625 + t = -3.930176721 Solving -3.90625 + t = -3.930176721 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 = -3.930176721 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = -3.930176721 + 3.90625 t = -3.930176721 + 3.90625 Combine like terms: -3.930176721 + 3.90625 = -0.023926721 t = -0.023926721 Simplifying t = -0.023926721Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.836426721, -0.023926721}
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