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Simplifying log(3x) + -2x2 + 8x + 16 = log(x + 4) Remove parenthesis around (3x) glo * 3x + -2x2 + 8x + 16 = log(x + 4) Reorder the terms for easier multiplication: 3glo * x + -2x2 + 8x + 16 = log(x + 4) Multiply glo * x 3glox + -2x2 + 8x + 16 = log(x + 4) Reorder the terms: 16 + 3glox + 8x + -2x2 = log(x + 4) Reorder the terms: 16 + 3glox + 8x + -2x2 = glo(4 + x) 16 + 3glox + 8x + -2x2 = (4 * glo + x * glo) 16 + 3glox + 8x + -2x2 = (4glo + glox) Solving 16 + 3glox + 8x + -2x2 = 4glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. 16 + 3glox + 8x + -4glo + -2x2 = 4glo + -4glo + glox Reorder the terms: 16 + -4glo + 3glox + 8x + -2x2 = 4glo + -4glo + glox Combine like terms: 4glo + -4glo = 0 16 + -4glo + 3glox + 8x + -2x2 = 0 + glox 16 + -4glo + 3glox + 8x + -2x2 = glox Add '-1glox' to each side of the equation. 16 + -4glo + 3glox + 8x + -1glox + -2x2 = glox + -1glox Reorder the terms: 16 + -4glo + 3glox + -1glox + 8x + -2x2 = glox + -1glox Combine like terms: 3glox + -1glox = 2glox 16 + -4glo + 2glox + 8x + -2x2 = glox + -1glox Combine like terms: glox + -1glox = 0 16 + -4glo + 2glox + 8x + -2x2 = 0 Add '-16' to each side of the equation. 16 + -4glo + 2glox + 8x + -16 + -2x2 = 0 + -16 Reorder the terms: 16 + -16 + -4glo + 2glox + 8x + -2x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -4glo + 2glox + 8x + -2x2 = 0 + -16 -4glo + 2glox + 8x + -2x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -4glo + 2glox + 8x + -2x2 = -16 Add '-8x' to each side of the equation. -4glo + 2glox + 8x + -8x + -2x2 = -16 + -8x Combine like terms: 8x + -8x = 0 -4glo + 2glox + 0 + -2x2 = -16 + -8x -4glo + 2glox + -2x2 = -16 + -8x Add '2x2' to each side of the equation. -4glo + 2glox + -2x2 + 2x2 = -16 + -8x + 2x2 Combine like terms: -2x2 + 2x2 = 0 -4glo + 2glox + 0 = -16 + -8x + 2x2 -4glo + 2glox = -16 + -8x + 2x2 Reorder the terms: 16 + -4glo + 2glox + 8x + -2x2 = -16 + -8x + 2x2 + 16 + 8x + -2x2 Reorder the terms: 16 + -4glo + 2glox + 8x + -2x2 = -16 + 16 + -8x + 8x + 2x2 + -2x2 Combine like terms: -16 + 16 = 0 16 + -4glo + 2glox + 8x + -2x2 = 0 + -8x + 8x + 2x2 + -2x2 16 + -4glo + 2glox + 8x + -2x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 16 + -4glo + 2glox + 8x + -2x2 = 0 + 2x2 + -2x2 16 + -4glo + 2glox + 8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 16 + -4glo + 2glox + 8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -2glo + glox + 4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -2glo + glox + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 8 + -2glo + glox + 4x + -1x2 = 0 Solving 8 + -2glo + glox + 4x + -1x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -2glo + glox + 4x + -8 + -1x2 = 0 + -8 Reorder the terms: 8 + -8 + -2glo + glox + 4x + -1x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -2glo + glox + 4x + -1x2 = 0 + -8 -2glo + glox + 4x + -1x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -2glo + glox + 4x + -1x2 = -8 Add '-4x' to each side of the equation. -2glo + glox + 4x + -4x + -1x2 = -8 + -4x Combine like terms: 4x + -4x = 0 -2glo + glox + 0 + -1x2 = -8 + -4x -2glo + glox + -1x2 = -8 + -4x Add 'x2' to each side of the equation. -2glo + glox + -1x2 + x2 = -8 + -4x + x2 Combine like terms: -1x2 + x2 = 0 -2glo + glox + 0 = -8 + -4x + x2 -2glo + glox = -8 + -4x + x2 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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