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Simplifying 6400t2 + 20t + -1 = 0 Reorder the terms: -1 + 20t + 6400t2 = 0 Solving -1 + 20t + 6400t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 6400 the coefficient of the squared term: Divide each side by '6400'. -0.00015625 + 0.003125t + t2 = 0 Move the constant term to the right: Add '0.00015625' to each side of the equation. -0.00015625 + 0.003125t + 0.00015625 + t2 = 0 + 0.00015625 Reorder the terms: -0.00015625 + 0.00015625 + 0.003125t + t2 = 0 + 0.00015625 Combine like terms: -0.00015625 + 0.00015625 = 0.00000000 0.00000000 + 0.003125t + t2 = 0 + 0.00015625 0.003125t + t2 = 0 + 0.00015625 Combine like terms: 0 + 0.00015625 = 0.00015625 0.003125t + t2 = 0.00015625 The t term is 0.003125t. Take half its coefficient (0.0015625). Square it (0.00000244140625) and add it to both sides. Add '0.00000244140625' to each side of the equation. 0.003125t + 0.00000244140625 + t2 = 0.00015625 + 0.00000244140625 Reorder the terms: 0.00000244140625 + 0.003125t + t2 = 0.00015625 + 0.00000244140625 Combine like terms: 0.00015625 + 0.00000244140625 = 0.00015869140625 0.00000244140625 + 0.003125t + t2 = 0.00015869140625 Factor a perfect square on the left side: (t + 0.0015625)(t + 0.0015625) = 0.00015869140625 Calculate the square root of the right side: 0.012597278 Break this problem into two subproblems by setting (t + 0.0015625) equal to 0.012597278 and -0.012597278.Subproblem 1
t + 0.0015625 = 0.012597278 Simplifying t + 0.0015625 = 0.012597278 Reorder the terms: 0.0015625 + t = 0.012597278 Solving 0.0015625 + t = 0.012597278 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0015625' to each side of the equation. 0.0015625 + -0.0015625 + t = 0.012597278 + -0.0015625 Combine like terms: 0.0015625 + -0.0015625 = 0.0000000 0.0000000 + t = 0.012597278 + -0.0015625 t = 0.012597278 + -0.0015625 Combine like terms: 0.012597278 + -0.0015625 = 0.011034778 t = 0.011034778 Simplifying t = 0.011034778Subproblem 2
t + 0.0015625 = -0.012597278 Simplifying t + 0.0015625 = -0.012597278 Reorder the terms: 0.0015625 + t = -0.012597278 Solving 0.0015625 + t = -0.012597278 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0015625' to each side of the equation. 0.0015625 + -0.0015625 + t = -0.012597278 + -0.0015625 Combine like terms: 0.0015625 + -0.0015625 = 0.0000000 0.0000000 + t = -0.012597278 + -0.0015625 t = -0.012597278 + -0.0015625 Combine like terms: -0.012597278 + -0.0015625 = -0.014159778 t = -0.014159778 Simplifying t = -0.014159778Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.011034778, -0.014159778}
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