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Simplifying y[n + 2] + -0.75y[n + 1] + 0.125y[n] = 0.25x[n + 1] Reorder the terms: y[2 + n] + -0.75y[n + 1] + 0.125y[n] = 0.25x[n + 1] [2 * y + n * y] + -0.75y[n + 1] + 0.125y[n] = 0.25x[n + 1] Reorder the terms: [ny + 2y] + -0.75y[n + 1] + 0.125y[n] = 0.25x[n + 1] [ny + 2y] + -0.75y[n + 1] + 0.125y[n] = 0.25x[n + 1] Reorder the terms: ny + 2y + -0.75y[1 + n] + 0.125y[n] = 0.25x[n + 1] ny + 2y + [1 * -0.75y + n * -0.75y] + 0.125y[n] = 0.25x[n + 1] Reorder the terms: ny + 2y + [-0.75ny + -0.75y] + 0.125y[n] = 0.25x[n + 1] ny + 2y + [-0.75ny + -0.75y] + 0.125y[n] = 0.25x[n + 1] Multiply y * n ny + 2y + -0.75ny + -0.75y + 0.125ny = 0.25x[n + 1] Reorder the terms: ny + -0.75ny + 0.125ny + 2y + -0.75y = 0.25x[n + 1] Combine like terms: ny + -0.75ny = 0.25ny 0.25ny + 0.125ny + 2y + -0.75y = 0.25x[n + 1] Combine like terms: 0.25ny + 0.125ny = 0.375ny 0.375ny + 2y + -0.75y = 0.25x[n + 1] Combine like terms: 2y + -0.75y = 1.25y 0.375ny + 1.25y = 0.25x[n + 1] Reorder the terms: 0.375ny + 1.25y = 0.25x[1 + n] 0.375ny + 1.25y = [1 * 0.25x + n * 0.25x] Reorder the terms: 0.375ny + 1.25y = [0.25nx + 0.25x] 0.375ny + 1.25y = [0.25nx + 0.25x] Solving 0.375ny + 1.25y = 0.25nx + 0.25x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.25nx' to each side of the equation. 0.375ny + -0.25nx + 1.25y = 0.25nx + -0.25nx + 0.25x Reorder the terms: -0.25nx + 0.375ny + 1.25y = 0.25nx + -0.25nx + 0.25x Combine like terms: 0.25nx + -0.25nx = 0.00 -0.25nx + 0.375ny + 1.25y = 0.00 + 0.25x -0.25nx + 0.375ny + 1.25y = 0.25x Add '-1.25y' to each side of the equation. -0.25nx + 0.375ny + 1.25y + -1.25y = 0.25x + -1.25y Combine like terms: 1.25y + -1.25y = 0.00 -0.25nx + 0.375ny + 0.00 = 0.25x + -1.25y -0.25nx + 0.375ny = 0.25x + -1.25y Reorder the terms: -0.25nx + 0.375ny + -0.25x + 1.25y = 0.25x + -0.25x + -1.25y + 1.25y Combine like terms: 0.25x + -0.25x = 0.00 -0.25nx + 0.375ny + -0.25x + 1.25y = 0.00 + -1.25y + 1.25y -0.25nx + 0.375ny + -0.25x + 1.25y = -1.25y + 1.25y Combine like terms: -1.25y + 1.25y = 0.00 -0.25nx + 0.375ny + -0.25x + 1.25y = 0.00 The solution to this equation could not be determined.
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