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Simplifying 64n2 + -50n + -1 = 0 Reorder the terms: -1 + -50n + 64n2 = 0 Solving -1 + -50n + 64n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.015625 + -0.78125n + n2 = 0 Move the constant term to the right: Add '0.015625' to each side of the equation. -0.015625 + -0.78125n + 0.015625 + n2 = 0 + 0.015625 Reorder the terms: -0.015625 + 0.015625 + -0.78125n + n2 = 0 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + -0.78125n + n2 = 0 + 0.015625 -0.78125n + n2 = 0 + 0.015625 Combine like terms: 0 + 0.015625 = 0.015625 -0.78125n + n2 = 0.015625 The n term is -0.78125n. Take half its coefficient (-0.390625). Square it (0.1525878906) and add it to both sides. Add '0.1525878906' to each side of the equation. -0.78125n + 0.1525878906 + n2 = 0.015625 + 0.1525878906 Reorder the terms: 0.1525878906 + -0.78125n + n2 = 0.015625 + 0.1525878906 Combine like terms: 0.015625 + 0.1525878906 = 0.1682128906 0.1525878906 + -0.78125n + n2 = 0.1682128906 Factor a perfect square on the left side: (n + -0.390625)(n + -0.390625) = 0.1682128906 Calculate the square root of the right side: 0.410137648 Break this problem into two subproblems by setting (n + -0.390625) equal to 0.410137648 and -0.410137648.Subproblem 1
n + -0.390625 = 0.410137648 Simplifying n + -0.390625 = 0.410137648 Reorder the terms: -0.390625 + n = 0.410137648 Solving -0.390625 + n = 0.410137648 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.390625' to each side of the equation. -0.390625 + 0.390625 + n = 0.410137648 + 0.390625 Combine like terms: -0.390625 + 0.390625 = 0.000000 0.000000 + n = 0.410137648 + 0.390625 n = 0.410137648 + 0.390625 Combine like terms: 0.410137648 + 0.390625 = 0.800762648 n = 0.800762648 Simplifying n = 0.800762648Subproblem 2
n + -0.390625 = -0.410137648 Simplifying n + -0.390625 = -0.410137648 Reorder the terms: -0.390625 + n = -0.410137648 Solving -0.390625 + n = -0.410137648 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.390625' to each side of the equation. -0.390625 + 0.390625 + n = -0.410137648 + 0.390625 Combine like terms: -0.390625 + 0.390625 = 0.000000 0.000000 + n = -0.410137648 + 0.390625 n = -0.410137648 + 0.390625 Combine like terms: -0.410137648 + 0.390625 = -0.019512648 n = -0.019512648 Simplifying n = -0.019512648Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.800762648, -0.019512648}
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