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Simplifying lnx(x + -7)(x + 7) = 0 Reorder the terms: lnx(-7 + x)(x + 7) = 0 Reorder the terms: lnx(-7 + x)(7 + x) = 0 Multiply (-7 + x) * (7 + x) lnx(-7(7 + x) + x(7 + x)) = 0 lnx((7 * -7 + x * -7) + x(7 + x)) = 0 lnx((-49 + -7x) + x(7 + x)) = 0 lnx(-49 + -7x + (7 * x + x * x)) = 0 lnx(-49 + -7x + (7x + x2)) = 0 Combine like terms: -7x + 7x = 0 lnx(-49 + 0 + x2) = 0 lnx(-49 + x2) = 0 (-49 * lnx + x2 * lnx) = 0 (-49lnx + lnx3) = 0 Solving -49lnx + lnx3 = 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), 'lnx'. lnx(-49 + x2) = 0 Factor a difference between two squares. lnx((7 + x)(-7 + x)) = 0Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -1x 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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