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Simplifying -16t2 + 116t + 101 = 0 Reorder the terms: 101 + 116t + -16t2 = 0 Solving 101 + 116t + -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'. -6.3125 + -7.25t + t2 = 0 Move the constant term to the right: Add '6.3125' to each side of the equation. -6.3125 + -7.25t + 6.3125 + t2 = 0 + 6.3125 Reorder the terms: -6.3125 + 6.3125 + -7.25t + t2 = 0 + 6.3125 Combine like terms: -6.3125 + 6.3125 = 0.0000 0.0000 + -7.25t + t2 = 0 + 6.3125 -7.25t + t2 = 0 + 6.3125 Combine like terms: 0 + 6.3125 = 6.3125 -7.25t + t2 = 6.3125 The t term is -7.25t. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25t + 13.140625 + t2 = 6.3125 + 13.140625 Reorder the terms: 13.140625 + -7.25t + t2 = 6.3125 + 13.140625 Combine like terms: 6.3125 + 13.140625 = 19.453125 13.140625 + -7.25t + t2 = 19.453125 Factor a perfect square on the left side: (t + -3.625)(t + -3.625) = 19.453125 Calculate the square root of the right side: 4.410569691 Break this problem into two subproblems by setting (t + -3.625) equal to 4.410569691 and -4.410569691.Subproblem 1
t + -3.625 = 4.410569691 Simplifying t + -3.625 = 4.410569691 Reorder the terms: -3.625 + t = 4.410569691 Solving -3.625 + t = 4.410569691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + t = 4.410569691 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + t = 4.410569691 + 3.625 t = 4.410569691 + 3.625 Combine like terms: 4.410569691 + 3.625 = 8.035569691 t = 8.035569691 Simplifying t = 8.035569691Subproblem 2
t + -3.625 = -4.410569691 Simplifying t + -3.625 = -4.410569691 Reorder the terms: -3.625 + t = -4.410569691 Solving -3.625 + t = -4.410569691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + t = -4.410569691 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + t = -4.410569691 + 3.625 t = -4.410569691 + 3.625 Combine like terms: -4.410569691 + 3.625 = -0.785569691 t = -0.785569691 Simplifying t = -0.785569691Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.035569691, -0.785569691}
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