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Simplifying lg((2x2) + -7) = 2lg(x + -1) Reorder the terms: gl(-7 + (2x2)) = 2lg(x + -1) (-7 * gl + (2x2) * gl) = 2lg(x + -1) (-7gl + 2glx2) = 2lg(x + -1) Reorder the terms: -7gl + 2glx2 = 2gl(-1 + x) -7gl + 2glx2 = (-1 * 2gl + x * 2gl) -7gl + 2glx2 = (-2gl + 2glx) Solving -7gl + 2glx2 = -2gl + 2glx 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. -7gl + 2gl + 2glx2 = -2gl + 2gl + 2glx Combine like terms: -7gl + 2gl = -5gl -5gl + 2glx2 = -2gl + 2gl + 2glx Combine like terms: -2gl + 2gl = 0 -5gl + 2glx2 = 0 + 2glx -5gl + 2glx2 = 2glx Add '-2glx' to each side of the equation. -5gl + -2glx + 2glx2 = 2glx + -2glx Combine like terms: 2glx + -2glx = 0 -5gl + -2glx + 2glx2 = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(-5 + -2x + 2x2) = 0Subproblem 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 '(-5 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + -2x + 2x2 = 0 Solving -5 + -2x + 2x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -2x + 5 + 2x2 = 0 + 5 Reorder the terms: -5 + 5 + -2x + 2x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x + 2x2 = 0 + 5 -2x + 2x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x + 2x2 = 5 Add '2x' to each side of the equation. -2x + 2x + 2x2 = 5 + 2x Combine like terms: -2x + 2x = 0 0 + 2x2 = 5 + 2x 2x2 = 5 + 2x Add '-2x2' to each side of the equation. 2x2 + -2x2 = 5 + 2x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = 5 + 2x + -2x2 Simplifying 0 = 5 + 2x + -2x2 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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