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Simplifying 54x5 + 9x4 + -165x3 = 0 Reorder the terms: -165x3 + 9x4 + 54x5 = 0 Solving -165x3 + 9x4 + 54x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x3'. 3x3(-55 + 3x + 18x2) = 0 Factor a trinomial. 3x3((-11 + -6x)(5 + -3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(-11 + -6x)' equal to zero and attempt to solve: Simplifying -11 + -6x = 0 Solving -11 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -6x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -6x = 0 + 11 -6x = 0 + 11 Combine like terms: 0 + 11 = 11 -6x = 11 Divide each side by '-6'. x = -1.833333333 Simplifying x = -1.833333333Subproblem 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 = 1.666666667Solution
x = {-1.833333333, 1.666666667}
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