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Simplifying lg(x + -10) * lg(x + 10) = 0 Reorder the terms: gl(-10 + x) * lg(x + 10) = 0 Reorder the terms: gl(-10 + x) * gl(10 + x) = 0 Reorder the terms for easier multiplication: gl * gl(-10 + x)(10 + x) = 0 Multiply gl * gl g2l2(-10 + x)(10 + x) = 0 Multiply (-10 + x) * (10 + x) g2l2(-10(10 + x) + x(10 + x)) = 0 g2l2((10 * -10 + x * -10) + x(10 + x)) = 0 g2l2((-100 + -10x) + x(10 + x)) = 0 g2l2(-100 + -10x + (10 * x + x * x)) = 0 g2l2(-100 + -10x + (10x + x2)) = 0 Combine like terms: -10x + 10x = 0 g2l2(-100 + 0 + x2) = 0 g2l2(-100 + x2) = 0 (-100 * g2l2 + x2 * g2l2) = 0 (-100g2l2 + g2l2x2) = 0 Solving -100g2l2 + g2l2x2 = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'g2l2'. g2l2(-100 + x2) = 0 Factor a difference between two squares. g2l2((10 + x)(-10 + x)) = 0Subproblem 1
Set the factor 'g2l2' equal to zero and attempt to solve: Simplifying g2l2 = 0 Solving g2l2 = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g2l2 = 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -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 '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Add '-1x' to each side of the equation. x + -1x = 10 + -1x Combine like terms: x + -1x = 0 0 = 10 + -1x Simplifying 0 = 10 + -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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