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Simplifying lg(9x + -1x2) = lg(x2 + -1x + -2) (9x * gl + -1x2 * gl) = lg(x2 + -1x + -2) (9glx + -1glx2) = lg(x2 + -1x + -2) Reorder the terms: 9glx + -1glx2 = gl(-2 + -1x + x2) 9glx + -1glx2 = (-2 * gl + -1x * gl + x2 * gl) 9glx + -1glx2 = (-2gl + -1glx + glx2) Solving 9glx + -1glx2 = -2gl + -1glx + glx2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2gl' to each side of the equation. 9glx + 2gl + -1glx2 = -2gl + -1glx + 2gl + glx2 Reorder the terms: 2gl + 9glx + -1glx2 = -2gl + -1glx + 2gl + glx2 Reorder the terms: 2gl + 9glx + -1glx2 = -2gl + 2gl + -1glx + glx2 Combine like terms: -2gl + 2gl = 0 2gl + 9glx + -1glx2 = 0 + -1glx + glx2 2gl + 9glx + -1glx2 = -1glx + glx2 Add 'glx' to each side of the equation. 2gl + 9glx + glx + -1glx2 = -1glx + glx + glx2 Combine like terms: 9glx + glx = 10glx 2gl + 10glx + -1glx2 = -1glx + glx + glx2 Combine like terms: -1glx + glx = 0 2gl + 10glx + -1glx2 = 0 + glx2 2gl + 10glx + -1glx2 = glx2 Add '-1glx2' to each side of the equation. 2gl + 10glx + -1glx2 + -1glx2 = glx2 + -1glx2 Combine like terms: -1glx2 + -1glx2 = -2glx2 2gl + 10glx + -2glx2 = glx2 + -1glx2 Combine like terms: glx2 + -1glx2 = 0 2gl + 10glx + -2glx2 = 0 Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(1 + 5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 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 '(1 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + -1x2 = 0 Solving 1 + 5x + -1x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 5x + -1 + -1x2 = 0 + -1 Reorder the terms: 1 + -1 + 5x + -1x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x + -1x2 = 0 + -1 5x + -1x2 = 0 + -1 Combine like terms: 0 + -1 = -1 5x + -1x2 = -1 Add '-5x' to each side of the equation. 5x + -5x + -1x2 = -1 + -5x Combine like terms: 5x + -5x = 0 0 + -1x2 = -1 + -5x -1x2 = -1 + -5x Add 'x2' to each side of the equation. -1x2 + x2 = -1 + -5x + x2 Combine like terms: -1x2 + x2 = 0 0 = -1 + -5x + x2 Simplifying 0 = -1 + -5x + 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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