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Simplifying x5 + 9x4 + 27x3 = 0 Reorder the terms: 27x3 + 9x4 + x5 = 0 Solving 27x3 + 9x4 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(27 + 9x + x2) = 0Subproblem 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 '(27 + 9x + x2)' equal to zero and attempt to solve: Simplifying 27 + 9x + x2 = 0 Solving 27 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 9x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 9x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 9x + x2 = 0 + -27 9x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 9x + x2 = -27 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -27 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -27 + 20.25 Combine like terms: -27 + 20.25 = -6.75 20.25 + 9x + x2 = -6.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = -6.75 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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