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Simplifying 8t2 + -1t + -28 = 0 Reorder the terms: -28 + -1t + 8t2 = 0 Solving -28 + -1t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.5 + -0.125t + t2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.125t + 3.5 + t2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.125t + t2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.125t + t2 = 0 + 3.5 -0.125t + t2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.125t + t2 = 3.5 The t term is -0.125t. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125t + 0.00390625 + t2 = 3.5 + 0.00390625 Reorder the terms: 0.00390625 + -0.125t + t2 = 3.5 + 0.00390625 Combine like terms: 3.5 + 0.00390625 = 3.50390625 0.00390625 + -0.125t + t2 = 3.50390625 Factor a perfect square on the left side: (t + -0.0625)(t + -0.0625) = 3.50390625 Calculate the square root of the right side: 1.871872391 Break this problem into two subproblems by setting (t + -0.0625) equal to 1.871872391 and -1.871872391.Subproblem 1
t + -0.0625 = 1.871872391 Simplifying t + -0.0625 = 1.871872391 Reorder the terms: -0.0625 + t = 1.871872391 Solving -0.0625 + t = 1.871872391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + t = 1.871872391 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + t = 1.871872391 + 0.0625 t = 1.871872391 + 0.0625 Combine like terms: 1.871872391 + 0.0625 = 1.934372391 t = 1.934372391 Simplifying t = 1.934372391Subproblem 2
t + -0.0625 = -1.871872391 Simplifying t + -0.0625 = -1.871872391 Reorder the terms: -0.0625 + t = -1.871872391 Solving -0.0625 + t = -1.871872391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + t = -1.871872391 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + t = -1.871872391 + 0.0625 t = -1.871872391 + 0.0625 Combine like terms: -1.871872391 + 0.0625 = -1.809372391 t = -1.809372391 Simplifying t = -1.809372391Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.934372391, -1.809372391}
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