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Simplifying 5 + 50t + -16t2 = 0 Solving 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'. -0.3125 + -3.125t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -3.125t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -3.125t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -3.125t + t2 = 0 + 0.3125 -3.125t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -3.125t + t2 = 0.3125 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 = 0.3125 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 0.3125 + 2.44140625 Combine like terms: 0.3125 + 2.44140625 = 2.75390625 2.44140625 + -3.125t + t2 = 2.75390625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 2.75390625 Calculate the square root of the right side: 1.659489756 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.659489756 and -1.659489756.Subproblem 1
t + -1.5625 = 1.659489756 Simplifying t + -1.5625 = 1.659489756 Reorder the terms: -1.5625 + t = 1.659489756 Solving -1.5625 + t = 1.659489756 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 = 1.659489756 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.659489756 + 1.5625 t = 1.659489756 + 1.5625 Combine like terms: 1.659489756 + 1.5625 = 3.221989756 t = 3.221989756 Simplifying t = 3.221989756Subproblem 2
t + -1.5625 = -1.659489756 Simplifying t + -1.5625 = -1.659489756 Reorder the terms: -1.5625 + t = -1.659489756 Solving -1.5625 + t = -1.659489756 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 = -1.659489756 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.659489756 + 1.5625 t = -1.659489756 + 1.5625 Combine like terms: -1.659489756 + 1.5625 = -0.096989756 t = -0.096989756 Simplifying t = -0.096989756Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.221989756, -0.096989756}
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