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Simplifying log(9)(-11x + 2) = log(9)(x2 + 30) Reorder the terms: glo * 9(2 + -11x) = log(9)(x2 + 30) Reorder the terms for easier multiplication: 9glo(2 + -11x) = log(9)(x2 + 30) (2 * 9glo + -11x * 9glo) = log(9)(x2 + 30) (18glo + -99glox) = log(9)(x2 + 30) Reorder the terms: 18glo + -99glox = glo * 9(30 + x2) Reorder the terms for easier multiplication: 18glo + -99glox = 9glo(30 + x2) 18glo + -99glox = (30 * 9glo + x2 * 9glo) 18glo + -99glox = (270glo + 9glox2) Solving 18glo + -99glox = 270glo + 9glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-270glo' to each side of the equation. 18glo + -270glo + -99glox = 270glo + -270glo + 9glox2 Combine like terms: 18glo + -270glo = -252glo -252glo + -99glox = 270glo + -270glo + 9glox2 Combine like terms: 270glo + -270glo = 0 -252glo + -99glox = 0 + 9glox2 -252glo + -99glox = 9glox2 Add '-9glox2' to each side of the equation. -252glo + -99glox + -9glox2 = 9glox2 + -9glox2 Combine like terms: 9glox2 + -9glox2 = 0 -252glo + -99glox + -9glox2 = 0 Factor out the Greatest Common Factor (GCF), '-9glo'. -9glo(28 + 11x + x2) = 0 Factor a trinomial. -9glo((7 + x)(4 + x)) = 0 Ignore the factor -9.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 g 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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