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Simplifying log[2](-14x + 1) = log[2](x2 + 50) Reorder the terms: glo * 2(1 + -14x) = log[2](x2 + 50) Reorder the terms for easier multiplication: 2glo(1 + -14x) = log[2](x2 + 50) (1 * 2glo + -14x * 2glo) = log[2](x2 + 50) (2glo + -28glox) = log[2](x2 + 50) Reorder the terms: 2glo + -28glox = glo * 2(50 + x2) Reorder the terms for easier multiplication: 2glo + -28glox = 2glo(50 + x2) 2glo + -28glox = (50 * 2glo + x2 * 2glo) 2glo + -28glox = (100glo + 2glox2) Solving 2glo + -28glox = 100glo + 2glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-100glo' to each side of the equation. 2glo + -100glo + -28glox = 100glo + -100glo + 2glox2 Combine like terms: 2glo + -100glo = -98glo -98glo + -28glox = 100glo + -100glo + 2glox2 Combine like terms: 100glo + -100glo = 0 -98glo + -28glox = 0 + 2glox2 -98glo + -28glox = 2glox2 Add '-2glox2' to each side of the equation. -98glo + -28glox + -2glox2 = 2glox2 + -2glox2 Combine like terms: 2glox2 + -2glox2 = 0 -98glo + -28glox + -2glox2 = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(49 + 14x + x2) = 0 Factor a trinomial. -2glo((7 + x)(7 + x)) = 0 Ignore the factor -2.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 '(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. The solution to this equation could not be determined.
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