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Simplifying (lnx)(lnx) + -1lnx + -6 = 0 Multiply lnx * lnx l2n2x2 + -1lnx + -6 = 0 Reorder the terms: -6 + -1lnx + l2n2x2 = 0 Solving -6 + -1lnx + l2n2x2 = 0 Solving for variable 'l'. Factor a trinomial. (-2 + -1lnx)(3 + -1lnx) = 0Subproblem 1
Set the factor '(-2 + -1lnx)' equal to zero and attempt to solve: Simplifying -2 + -1lnx = 0 Solving -2 + -1lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1lnx = 0 + 2 -1lnx = 0 + 2 Combine like terms: 0 + 2 = 2 -1lnx = 2 Divide each side by '-1nx'. l = -2n-1x-1 Simplifying l = -2n-1x-1Subproblem 2
Set the factor '(3 + -1lnx)' equal to zero and attempt to solve: Simplifying 3 + -1lnx = 0 Solving 3 + -1lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1lnx = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1lnx = 0 + -3 -1lnx = 0 + -3 Combine like terms: 0 + -3 = -3 -1lnx = -3 Divide each side by '-1nx'. l = 3n-1x-1 Simplifying l = 3n-1x-1Solution
l = {-2n-1x-1, 3n-1x-1}
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