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Simplifying y[n] + -0.5y[n + -1] + 0.06y[n + -2] = 5x[n] Multiply y * n ny + -0.5y[n + -1] + 0.06y[n + -2] = 5x[n] Reorder the terms: ny + -0.5y[-1 + n] + 0.06y[n + -2] = 5x[n] ny + [-1 * -0.5y + n * -0.5y] + 0.06y[n + -2] = 5x[n] Reorder the terms: ny + [-0.5ny + 0.5y] + 0.06y[n + -2] = 5x[n] ny + [-0.5ny + 0.5y] + 0.06y[n + -2] = 5x[n] Reorder the terms: ny + -0.5ny + 0.5y + 0.06y[-2 + n] = 5x[n] ny + -0.5ny + 0.5y + [-2 * 0.06y + n * 0.06y] = 5x[n] Reorder the terms: ny + -0.5ny + 0.5y + [0.06ny + -0.12y] = 5x[n] ny + -0.5ny + 0.5y + [0.06ny + -0.12y] = 5x[n] Reorder the terms: ny + -0.5ny + 0.06ny + 0.5y + -0.12y = 5x[n] Combine like terms: ny + -0.5ny = 0.5ny 0.5ny + 0.06ny + 0.5y + -0.12y = 5x[n] Combine like terms: 0.5ny + 0.06ny = 0.56ny 0.56ny + 0.5y + -0.12y = 5x[n] Combine like terms: 0.5y + -0.12y = 0.38y 0.56ny + 0.38y = 5x[n] Multiply x * n 0.56ny + 0.38y = 5nx Solving 0.56ny + 0.38y = 5nx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5nx' to each side of the equation. 0.56ny + -5nx + 0.38y = 5nx + -5nx Reorder the terms: -5nx + 0.56ny + 0.38y = 5nx + -5nx Combine like terms: 5nx + -5nx = 0 -5nx + 0.56ny + 0.38y = 0 Add '-0.38y' to each side of the equation. -5nx + 0.56ny + 0.38y + -0.38y = 0 + -0.38y Combine like terms: 0.38y + -0.38y = 0.00 -5nx + 0.56ny + 0.00 = 0 + -0.38y -5nx + 0.56ny = 0 + -0.38y Remove the zero: -5nx + 0.56ny = -0.38y Combine like terms: -0.38y + 0.38y = 0.00 -5nx + 0.56ny + 0.38y = 0.00 The solution to this equation could not be determined.
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