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Simplifying 54x5 + 18x4 + 9x3 = 0 Reorder the terms: 9x3 + 18x4 + 54x5 = 0 Solving 9x3 + 18x4 + 54x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9x3'. 9x3(1 + 2x + 6x2) = 0 Ignore the factor 9.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 '(1 + 2x + 6x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 6x2 = 0 Solving 1 + 2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.3333333333x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.3333333333x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + -0.1666666667 0.3333333333x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 0.3333333333x + x2 = -0.1666666667 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -0.1666666667 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.1666666667 + 0.02777777779 Combine like terms: -0.1666666667 + 0.02777777779 = -0.13888888891 0.02777777779 + 0.3333333333x + x2 = -0.13888888891 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -0.13888888891 Can't calculate square root of the right side. 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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