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Simplifying (1 + -1x) * ln(1 + -1x) + x = 0.136 Reorder the terms for easier multiplication: ln(1 + -1x)(1 + -1x) + x = 0.136 Multiply (1 + -1x) * (1 + -1x) ln(1(1 + -1x) + -1x * (1 + -1x)) + x = 0.136 ln((1 * 1 + -1x * 1) + -1x * (1 + -1x)) + x = 0.136 ln((1 + -1x) + -1x * (1 + -1x)) + x = 0.136 ln(1 + -1x + (1 * -1x + -1x * -1x)) + x = 0.136 ln(1 + -1x + (-1x + 1x2)) + x = 0.136 Combine like terms: -1x + -1x = -2x ln(1 + -2x + 1x2) + x = 0.136 (1 * ln + -2x * ln + 1x2 * ln) + x = 0.136 (1ln + -2lnx + 1lnx2) + x = 0.136 Solving 1ln + -2lnx + 1lnx2 + x = 0.136 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1x' to each side of the equation. 1ln + -2lnx + 1lnx2 + x + -1x = 0.136 + -1x Combine like terms: x + -1x = 0 1ln + -2lnx + 1lnx2 + 0 = 0.136 + -1x 1ln + -2lnx + 1lnx2 = 0.136 + -1x Reorder the terms: -0.136 + 1ln + -2lnx + 1lnx2 + x = 0.136 + -1x + -0.136 + x Reorder the terms: -0.136 + 1ln + -2lnx + 1lnx2 + x = 0.136 + -0.136 + -1x + x Combine like terms: 0.136 + -0.136 = 0.000 -0.136 + 1ln + -2lnx + 1lnx2 + x = 0.000 + -1x + x -0.136 + 1ln + -2lnx + 1lnx2 + x = -1x + x Combine like terms: -1x + x = 0 -0.136 + 1ln + -2lnx + 1lnx2 + x = 0 The solution to this equation could not be determined.
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