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Simplifying f(x + 1) = x2 + 5x + -1 Reorder the terms: f(1 + x) = x2 + 5x + -1 (1 * f + x * f) = x2 + 5x + -1 (1f + fx) = x2 + 5x + -1 Reorder the terms: 1f + fx = -1 + 5x + x2 Solving 1f + fx = -1 + 5x + x2 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Reorder the terms: 1 + 1f + fx + -5x + -1x2 = -1 + 5x + x2 + 1 + -5x + -1x2 Reorder the terms: 1 + 1f + fx + -5x + -1x2 = -1 + 1 + 5x + -5x + x2 + -1x2 Combine like terms: -1 + 1 = 0 1 + 1f + fx + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 1 + 1f + fx + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 1 + 1f + fx + -5x + -1x2 = 0 + x2 + -1x2 1 + 1f + fx + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1 + 1f + fx + -5x + -1x2 = 0 The solution to this equation could not be determined.
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