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Simplifying 0 = x3 + -18x2 + 81x Reorder the terms: 0 = 81x + -18x2 + x3 Solving 0 = 81x + -18x2 + x3 Solving for variable 'x'. Remove the zero: -81x + 18x2 + -1x3 = 81x + -18x2 + x3 + -81x + 18x2 + -1x3 Reorder the terms: -81x + 18x2 + -1x3 = 81x + -81x + -18x2 + 18x2 + x3 + -1x3 Combine like terms: 81x + -81x = 0 -81x + 18x2 + -1x3 = 0 + -18x2 + 18x2 + x3 + -1x3 -81x + 18x2 + -1x3 = -18x2 + 18x2 + x3 + -1x3 Combine like terms: -18x2 + 18x2 = 0 -81x + 18x2 + -1x3 = 0 + x3 + -1x3 -81x + 18x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -81x + 18x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-81 + 18x + -1x2) = 0 Factor a trinomial. x((-9 + x)(9 + -1x)) = 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {0, 9, 9}
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