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Simplifying 64t2 + -16t + -1 = 0 Reorder the terms: -1 + -16t + 64t2 = 0 Solving -1 + -16t + 64t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.015625 + -0.25t + t2 = 0 Move the constant term to the right: Add '0.015625' to each side of the equation. -0.015625 + -0.25t + 0.015625 + t2 = 0 + 0.015625 Reorder the terms: -0.015625 + 0.015625 + -0.25t + t2 = 0 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + -0.25t + t2 = 0 + 0.015625 -0.25t + t2 = 0 + 0.015625 Combine like terms: 0 + 0.015625 = 0.015625 -0.25t + t2 = 0.015625 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = 0.015625 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 0.015625 + 0.015625 Combine like terms: 0.015625 + 0.015625 = 0.03125 0.015625 + -0.25t + t2 = 0.03125 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 0.03125 Calculate the square root of the right side: 0.176776695 Break this problem into two subproblems by setting (t + -0.125) equal to 0.176776695 and -0.176776695.Subproblem 1
t + -0.125 = 0.176776695 Simplifying t + -0.125 = 0.176776695 Reorder the terms: -0.125 + t = 0.176776695 Solving -0.125 + t = 0.176776695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 0.176776695 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 0.176776695 + 0.125 t = 0.176776695 + 0.125 Combine like terms: 0.176776695 + 0.125 = 0.301776695 t = 0.301776695 Simplifying t = 0.301776695Subproblem 2
t + -0.125 = -0.176776695 Simplifying t + -0.125 = -0.176776695 Reorder the terms: -0.125 + t = -0.176776695 Solving -0.125 + t = -0.176776695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -0.176776695 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -0.176776695 + 0.125 t = -0.176776695 + 0.125 Combine like terms: -0.176776695 + 0.125 = -0.051776695 t = -0.051776695 Simplifying t = -0.051776695Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.301776695, -0.051776695}
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