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Simplifying 81x5 = 625x Solving 81x5 = 625x Solving for variable 'x'. Reorder the terms: -625x + 81x5 = 625x + -625x Combine like terms: 625x + -625x = 0 -625x + 81x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-625 + 81x4) = 0 Factor a difference between two squares. x((25 + 9x2)(-25 + 9x2)) = 0 Factor a difference between two squares. x((25 + 9x2)((5 + 3x)(-5 + 3x))) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(25 + 9x2)' equal to zero and attempt to solve: Simplifying 25 + 9x2 = 0 Solving 25 + 9x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 9x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 9x2 = 0 + -25 9x2 = 0 + -25 Combine like terms: 0 + -25 = -25 9x2 = -25 Divide each side by '9'. x2 = -2.777777778 Simplifying x2 = -2.777777778 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 '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 4
Set the factor '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Divide each side by '3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {0, -1.666666667, 1.666666667}
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