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Simplifying x(k + 2) + -1x(k + 1) + x(k) = g(k) Reorder the terms: x(2 + k) + -1x(k + 1) + x(k) = g(k) (2 * x + k * x) + -1x(k + 1) + x(k) = g(k) Reorder the terms: (kx + 2x) + -1x(k + 1) + x(k) = g(k) (kx + 2x) + -1x(k + 1) + x(k) = g(k) Reorder the terms: kx + 2x + -1x(1 + k) + x(k) = g(k) kx + 2x + (1 * -1x + k * -1x) + x(k) = g(k) Reorder the terms: kx + 2x + (-1kx + -1x) + x(k) = g(k) kx + 2x + (-1kx + -1x) + x(k) = g(k) Multiply x * k kx + 2x + -1kx + -1x + kx = g(k) Reorder the terms: kx + -1kx + kx + 2x + -1x = g(k) Combine like terms: kx + -1kx = 0 0 + kx + 2x + -1x = g(k) kx + 2x + -1x = g(k) Combine like terms: 2x + -1x = 1x kx + 1x = g(k) Multiply g * k kx + 1x = gk Solving kx + 1x = gk Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1gk' to each side of the equation. kx + -1gk + 1x = gk + -1gk Reorder the terms: -1gk + kx + 1x = gk + -1gk Combine like terms: gk + -1gk = 0 -1gk + kx + 1x = 0 Add '-1x' to each side of the equation. -1gk + kx + 1x + -1x = 0 + -1x Combine like terms: 1x + -1x = 0 -1gk + kx + 0 = 0 + -1x -1gk + kx = 0 + -1x Remove the zero: -1gk + kx = -1x Combine like terms: -1x + x = 0 -1gk + kx + x = 0 The solution to this equation could not be determined.
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