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Simplifying (2ln(x) + 4)(x2 + -9) = 0 Multiply ln * x (2lnx + 4)(x2 + -9) = 0 Reorder the terms: (4 + 2lnx)(x2 + -9) = 0 Reorder the terms: (4 + 2lnx)(-9 + x2) = 0 Multiply (4 + 2lnx) * (-9 + x2) (4(-9 + x2) + 2lnx * (-9 + x2)) = 0 ((-9 * 4 + x2 * 4) + 2lnx * (-9 + x2)) = 0 ((-36 + 4x2) + 2lnx * (-9 + x2)) = 0 (-36 + 4x2 + (-9 * 2lnx + x2 * 2lnx)) = 0 (-36 + 4x2 + (-18lnx + 2lnx3)) = 0 Reorder the terms: (-36 + -18lnx + 2lnx3 + 4x2) = 0 (-36 + -18lnx + 2lnx3 + 4x2) = 0 Solving -36 + -18lnx + 2lnx3 + 4x2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '36' to each side of the equation. -36 + -18lnx + 2lnx3 + 36 + 4x2 = 0 + 36 Reorder the terms: -36 + 36 + -18lnx + 2lnx3 + 4x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -18lnx + 2lnx3 + 4x2 = 0 + 36 -18lnx + 2lnx3 + 4x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -18lnx + 2lnx3 + 4x2 = 36 Add '-4x2' to each side of the equation. -18lnx + 2lnx3 + 4x2 + -4x2 = 36 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -18lnx + 2lnx3 + 0 = 36 + -4x2 -18lnx + 2lnx3 = 36 + -4x2 Reorder the terms: -36 + -18lnx + 2lnx3 + 4x2 = 36 + -4x2 + -36 + 4x2 Reorder the terms: -36 + -18lnx + 2lnx3 + 4x2 = 36 + -36 + -4x2 + 4x2 Combine like terms: 36 + -36 = 0 -36 + -18lnx + 2lnx3 + 4x2 = 0 + -4x2 + 4x2 -36 + -18lnx + 2lnx3 + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -36 + -18lnx + 2lnx3 + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -9lnx + lnx3 + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -9lnx + lnx3 + 2x2)' equal to zero and attempt to solve: Simplifying -18 + -9lnx + lnx3 + 2x2 = 0 Solving -18 + -9lnx + lnx3 + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '18' to each side of the equation. -18 + -9lnx + lnx3 + 18 + 2x2 = 0 + 18 Reorder the terms: -18 + 18 + -9lnx + lnx3 + 2x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -9lnx + lnx3 + 2x2 = 0 + 18 -9lnx + lnx3 + 2x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -9lnx + lnx3 + 2x2 = 18 Add '-2x2' to each side of the equation. -9lnx + lnx3 + 2x2 + -2x2 = 18 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -9lnx + lnx3 + 0 = 18 + -2x2 -9lnx + lnx3 = 18 + -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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