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Simplifying 0 = -16t2 + 50t + 6.5 Reorder the terms: 0 = 6.5 + 50t + -16t2 Solving 0 = 6.5 + 50t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6.5 = -6.5 -6.5 + -50t + 16t2 = 6.5 + 50t + -16t2 + -6.5 + -50t + 16t2 Reorder the terms: -6.5 + -50t + 16t2 = 6.5 + -6.5 + 50t + -50t + -16t2 + 16t2 Combine like terms: 6.5 + -6.5 = 0.0 -6.5 + -50t + 16t2 = 0.0 + 50t + -50t + -16t2 + 16t2 -6.5 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 -6.5 + -50t + 16t2 = 0 + -16t2 + 16t2 -6.5 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6.5 + -50t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.40625 + -3.125t + t2 = 0 Move the constant term to the right: Add '0.40625' to each side of the equation. -0.40625 + -3.125t + 0.40625 + t2 = 0 + 0.40625 Reorder the terms: -0.40625 + 0.40625 + -3.125t + t2 = 0 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + -3.125t + t2 = 0 + 0.40625 -3.125t + t2 = 0 + 0.40625 Combine like terms: 0 + 0.40625 = 0.40625 -3.125t + t2 = 0.40625 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = 0.40625 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 0.40625 + 2.44140625 Combine like terms: 0.40625 + 2.44140625 = 2.84765625 2.44140625 + -3.125t + t2 = 2.84765625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 2.84765625 Calculate the square root of the right side: 1.6875 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.6875 and -1.6875.Subproblem 1
t + -1.5625 = 1.6875 Simplifying t + -1.5625 = 1.6875 Reorder the terms: -1.5625 + t = 1.6875 Solving -1.5625 + t = 1.6875 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 1.6875 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.6875 + 1.5625 t = 1.6875 + 1.5625 Combine like terms: 1.6875 + 1.5625 = 3.25 t = 3.25 Simplifying t = 3.25Subproblem 2
t + -1.5625 = -1.6875 Simplifying t + -1.5625 = -1.6875 Reorder the terms: -1.5625 + t = -1.6875 Solving -1.5625 + t = -1.6875 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -1.6875 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.6875 + 1.5625 t = -1.6875 + 1.5625 Combine like terms: -1.6875 + 1.5625 = -0.125 t = -0.125 Simplifying t = -0.125Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.25, -0.125}
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