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Simplifying -16t2 + 50t + 3.5 = 0 Reorder the terms: 3.5 + 50t + -16t2 = 0 Solving 3.5 + 50t + -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'. -0.21875 + -3.125t + t2 = 0 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + -3.125t + 0.21875 + t2 = 0 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + -3.125t + t2 = 0 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + -3.125t + t2 = 0 + 0.21875 -3.125t + t2 = 0 + 0.21875 Combine like terms: 0 + 0.21875 = 0.21875 -3.125t + t2 = 0.21875 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 = 0.21875 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 0.21875 + 2.44140625 Combine like terms: 0.21875 + 2.44140625 = 2.66015625 2.44140625 + -3.125t + t2 = 2.66015625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 2.66015625 Calculate the square root of the right side: 1.630998544 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.630998544 and -1.630998544.Subproblem 1
t + -1.5625 = 1.630998544 Simplifying t + -1.5625 = 1.630998544 Reorder the terms: -1.5625 + t = 1.630998544 Solving -1.5625 + t = 1.630998544 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 = 1.630998544 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.630998544 + 1.5625 t = 1.630998544 + 1.5625 Combine like terms: 1.630998544 + 1.5625 = 3.193498544 t = 3.193498544 Simplifying t = 3.193498544Subproblem 2
t + -1.5625 = -1.630998544 Simplifying t + -1.5625 = -1.630998544 Reorder the terms: -1.5625 + t = -1.630998544 Solving -1.5625 + t = -1.630998544 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 = -1.630998544 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.630998544 + 1.5625 t = -1.630998544 + 1.5625 Combine like terms: -1.630998544 + 1.5625 = -0.068498544 t = -0.068498544 Simplifying t = -0.068498544Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.193498544, -0.068498544}
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