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Simplifying ln(x2 + 9x + 14) + -1ln(x + 7) = 0 Reorder the terms: ln(14 + 9x + x2) + -1ln(x + 7) = 0 (14 * ln + 9x * ln + x2 * ln) + -1ln(x + 7) = 0 (14ln + 9lnx + lnx2) + -1ln(x + 7) = 0 Reorder the terms: 14ln + 9lnx + lnx2 + -1ln(7 + x) = 0 14ln + 9lnx + lnx2 + (7 * -1ln + x * -1ln) = 0 14ln + 9lnx + lnx2 + (-7ln + -1lnx) = 0 Reorder the terms: 14ln + -7ln + 9lnx + -1lnx + lnx2 = 0 Combine like terms: 14ln + -7ln = 7ln 7ln + 9lnx + -1lnx + lnx2 = 0 Combine like terms: 9lnx + -1lnx = 8lnx 7ln + 8lnx + lnx2 = 0 Solving 7ln + 8lnx + lnx2 = 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), 'ln'. ln(7 + 8x + x2) = 0 Factor a trinomial. ln((7 + x)(1 + 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 '(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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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