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Simplifying 0 = -16t2 + 5t + 50 Reorder the terms: 0 = 50 + 5t + -16t2 Solving 0 = 50 + 5t + -16t2 Solving for variable 't'. Combine like terms: 0 + -50 = -50 -50 + -5t + 16t2 = 50 + 5t + -16t2 + -50 + -5t + 16t2 Reorder the terms: -50 + -5t + 16t2 = 50 + -50 + 5t + -5t + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -50 + -5t + 16t2 = 0 + 5t + -5t + -16t2 + 16t2 -50 + -5t + 16t2 = 5t + -5t + -16t2 + 16t2 Combine like terms: 5t + -5t = 0 -50 + -5t + 16t2 = 0 + -16t2 + 16t2 -50 + -5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -50 + -5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.125 + -0.3125t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -0.3125t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -0.3125t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -0.3125t + t2 = 0 + 3.125 -0.3125t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -0.3125t + t2 = 3.125 The t term is -0.3125t. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125t + 0.0244140625 + t2 = 3.125 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 3.125 + 0.0244140625 Combine like terms: 3.125 + 0.0244140625 = 3.1494140625 0.0244140625 + -0.3125t + t2 = 3.1494140625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 3.1494140625 Calculate the square root of the right side: 1.774658858 Break this problem into two subproblems by setting (t + -0.15625) equal to 1.774658858 and -1.774658858.Subproblem 1
t + -0.15625 = 1.774658858 Simplifying t + -0.15625 = 1.774658858 Reorder the terms: -0.15625 + t = 1.774658858 Solving -0.15625 + t = 1.774658858 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 1.774658858 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 1.774658858 + 0.15625 t = 1.774658858 + 0.15625 Combine like terms: 1.774658858 + 0.15625 = 1.930908858 t = 1.930908858 Simplifying t = 1.930908858Subproblem 2
t + -0.15625 = -1.774658858 Simplifying t + -0.15625 = -1.774658858 Reorder the terms: -0.15625 + t = -1.774658858 Solving -0.15625 + t = -1.774658858 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -1.774658858 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -1.774658858 + 0.15625 t = -1.774658858 + 0.15625 Combine like terms: -1.774658858 + 0.15625 = -1.618408858 t = -1.618408858 Simplifying t = -1.618408858Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.930908858, -1.618408858}
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