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Simplifying log12(x2 + 35) = log12(-12x + -1) Reorder the terms: g12lo(35 + x2) = log12(-12x + -1) (35 * g12lo + x2 * g12lo) = log12(-12x + -1) (35g12lo + g12lox2) = log12(-12x + -1) Reorder the terms: 35g12lo + g12lox2 = g12lo(-1 + -12x) 35g12lo + g12lox2 = (-1 * g12lo + -12x * g12lo) 35g12lo + g12lox2 = (-1g12lo + -12g12lox) Solving 35g12lo + g12lox2 = -1g12lo + -12g12lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add 'g12lo' to each side of the equation. 35g12lo + g12lo + g12lox2 = -1g12lo + g12lo + -12g12lox Combine like terms: 35g12lo + g12lo = 36g12lo 36g12lo + g12lox2 = -1g12lo + g12lo + -12g12lox Combine like terms: -1g12lo + g12lo = 0 36g12lo + g12lox2 = 0 + -12g12lox 36g12lo + g12lox2 = -12g12lox Add '12g12lox' to each side of the equation. 36g12lo + 12g12lox + g12lox2 = -12g12lox + 12g12lox Combine like terms: -12g12lox + 12g12lox = 0 36g12lo + 12g12lox + g12lox2 = 0 Factor out the Greatest Common Factor (GCF), 'g12lo'. g12lo(36 + 12x + x2) = 0 Factor a trinomial. g12lo((6 + x)(6 + x)) = 0Subproblem 1
Set the factor 'g12lo' equal to zero and attempt to solve: Simplifying g12lo = 0 Solving g12lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g12lo = 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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