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Simplifying x * lnx + (x + -1) * ln(x + -1) = 0 Multiply x * lnx lnx2 + (x + -1) * ln(x + -1) = 0 Reorder the terms: lnx2 + (-1 + x) * ln(x + -1) = 0 Reorder the terms: lnx2 + (-1 + x) * ln(-1 + x) = 0 Reorder the terms for easier multiplication: lnx2 + ln(-1 + x)(-1 + x) = 0 Multiply (-1 + x) * (-1 + x) lnx2 + ln(-1(-1 + x) + x(-1 + x)) = 0 lnx2 + ln((-1 * -1 + x * -1) + x(-1 + x)) = 0 lnx2 + ln((1 + -1x) + x(-1 + x)) = 0 lnx2 + ln(1 + -1x + (-1 * x + x * x)) = 0 lnx2 + ln(1 + -1x + (-1x + x2)) = 0 Combine like terms: -1x + -1x = -2x lnx2 + ln(1 + -2x + x2) = 0 lnx2 + (1 * ln + -2x * ln + x2 * ln) = 0 lnx2 + (1ln + -2lnx + lnx2) = 0 Reorder the terms: 1ln + -2lnx + lnx2 + lnx2 = 0 Combine like terms: lnx2 + lnx2 = 2lnx2 1ln + -2lnx + 2lnx2 = 0 Solving 1ln + -2lnx + 2lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -2x + 2x2) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + -2x + 2x2 = 0 Solving 1 + -2x + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -2x + -1 + 2x2 = 0 + -1 Reorder the terms: 1 + -1 + -2x + 2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x + 2x2 = 0 + -1 -2x + 2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2x + 2x2 = -1 Add '2x' to each side of the equation. -2x + 2x + 2x2 = -1 + 2x Combine like terms: -2x + 2x = 0 0 + 2x2 = -1 + 2x 2x2 = -1 + 2x Add '-2x2' to each side of the equation. 2x2 + -2x2 = -1 + 2x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = -1 + 2x + -2x2 Simplifying 0 = -1 + 2x + -2x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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