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Simplifying ln(x + -5) + ln(x + 2) = ln(2x2 + -5x + -25) Reorder the terms: ln(-5 + x) + ln(x + 2) = ln(2x2 + -5x + -25) (-5 * ln + x * ln) + ln(x + 2) = ln(2x2 + -5x + -25) (-5ln + lnx) + ln(x + 2) = ln(2x2 + -5x + -25) Reorder the terms: -5ln + lnx + ln(2 + x) = ln(2x2 + -5x + -25) -5ln + lnx + (2 * ln + x * ln) = ln(2x2 + -5x + -25) -5ln + lnx + (2ln + lnx) = ln(2x2 + -5x + -25) Reorder the terms: -5ln + 2ln + lnx + lnx = ln(2x2 + -5x + -25) Combine like terms: -5ln + 2ln = -3ln -3ln + lnx + lnx = ln(2x2 + -5x + -25) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(2x2 + -5x + -25) Reorder the terms: -3ln + 2lnx = ln(-25 + -5x + 2x2) -3ln + 2lnx = (-25 * ln + -5x * ln + 2x2 * ln) -3ln + 2lnx = (-25ln + -5lnx + 2lnx2) Solving -3ln + 2lnx = -25ln + -5lnx + 2lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '25ln' to each side of the equation. -3ln + 25ln + 2lnx = -25ln + -5lnx + 25ln + 2lnx2 Combine like terms: -3ln + 25ln = 22ln 22ln + 2lnx = -25ln + -5lnx + 25ln + 2lnx2 Reorder the terms: 22ln + 2lnx = -25ln + 25ln + -5lnx + 2lnx2 Combine like terms: -25ln + 25ln = 0 22ln + 2lnx = 0 + -5lnx + 2lnx2 22ln + 2lnx = -5lnx + 2lnx2 Add '5lnx' to each side of the equation. 22ln + 2lnx + 5lnx = -5lnx + 5lnx + 2lnx2 Combine like terms: 2lnx + 5lnx = 7lnx 22ln + 7lnx = -5lnx + 5lnx + 2lnx2 Combine like terms: -5lnx + 5lnx = 0 22ln + 7lnx = 0 + 2lnx2 22ln + 7lnx = 2lnx2 Add '-2lnx2' to each side of the equation. 22ln + 7lnx + -2lnx2 = 2lnx2 + -2lnx2 Combine like terms: 2lnx2 + -2lnx2 = 0 22ln + 7lnx + -2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(22 + 7x + -2x2) = 0 Factor a trinomial. ln((11 + -2x)(2 + x)) = 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 '(11 + -2x)' equal to zero and attempt to solve: Simplifying 11 + -2x = 0 Solving 11 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2x = 0 + -11 -2x = 0 + -11 Combine like terms: 0 + -11 = -11 -2x = -11 Add '2x' to each side of the equation. -2x + 2x = -11 + 2x Combine like terms: -2x + 2x = 0 0 = -11 + 2x Simplifying 0 = -11 + 2x 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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