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Simplifying 0 = -16T2 + 116T + 101 Reorder the terms: 0 = 101 + 116T + -16T2 Solving 0 = 101 + 116T + -16T2 Solving for variable 'T'. Combine like terms: 0 + -101 = -101 -101 + -116T + 16T2 = 101 + 116T + -16T2 + -101 + -116T + 16T2 Reorder the terms: -101 + -116T + 16T2 = 101 + -101 + 116T + -116T + -16T2 + 16T2 Combine like terms: 101 + -101 = 0 -101 + -116T + 16T2 = 0 + 116T + -116T + -16T2 + 16T2 -101 + -116T + 16T2 = 116T + -116T + -16T2 + 16T2 Combine like terms: 116T + -116T = 0 -101 + -116T + 16T2 = 0 + -16T2 + 16T2 -101 + -116T + 16T2 = -16T2 + 16T2 Combine like terms: -16T2 + 16T2 = 0 -101 + -116T + 16T2 = 0 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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