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Simplifying lx(x + 8) + ln(x + -1) = 2lnx Reorder the terms: lx(8 + x) + ln(x + -1) = 2lnx (8 * lx + x * lx) + ln(x + -1) = 2lnx (8lx + lx2) + ln(x + -1) = 2lnx Reorder the terms: 8lx + lx2 + ln(-1 + x) = 2lnx 8lx + lx2 + (-1 * ln + x * ln) = 2lnx 8lx + lx2 + (-1ln + lnx) = 2lnx Reorder the terms: -1ln + lnx + 8lx + lx2 = 2lnx Solving -1ln + lnx + 8lx + lx2 = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. -1ln + lnx + 8lx + -2lnx + lx2 = 2lnx + -2lnx Reorder the terms: -1ln + lnx + -2lnx + 8lx + lx2 = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -1ln + -1lnx + 8lx + lx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -1ln + -1lnx + 8lx + lx2 = 0 Factor out the Greatest Common Factor (GCF), 'l'. l(-1n + -1nx + 8x + x2) = 0Subproblem 1
Set the factor 'l' equal to zero and attempt to solve: Simplifying l = 0 Solving l = 0 Move all terms containing l to the left, all other terms to the right. Simplifying l = 0Subproblem 2
Set the factor '(-1n + -1nx + 8x + x2)' equal to zero and attempt to solve: Simplifying -1n + -1nx + 8x + x2 = 0 Solving -1n + -1nx + 8x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add 'n' to each side of the equation. -1n + -1nx + 8x + n + x2 = 0 + n Reorder the terms: -1n + n + -1nx + 8x + x2 = 0 + n Combine like terms: -1n + n = 0 0 + -1nx + 8x + x2 = 0 + n -1nx + 8x + x2 = 0 + n Remove the zero: -1nx + 8x + x2 = n Add 'nx' to each side of the equation. -1nx + 8x + nx + x2 = n + nx Reorder the terms: -1nx + nx + 8x + x2 = n + nx Combine like terms: -1nx + nx = 0 0 + 8x + x2 = n + nx 8x + x2 = n + nx Add '-8x' to each side of the equation. 8x + -8x + x2 = n + nx + -8x Combine like terms: 8x + -8x = 0 0 + x2 = n + nx + -8x x2 = n + nx + -8x Add '-1x2' to each side of the equation. x2 + -1x2 = n + nx + -8x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = n + nx + -8x + -1x2 Simplifying 0 = n + nx + -8x + -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
l = {0}
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