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Simplifying 3n3 + -33n2 + 99n = 0 Reorder the terms: 99n + -33n2 + 3n3 = 0 Solving 99n + -33n2 + 3n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(33 + -11n + n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(33 + -11n + n2)' equal to zero and attempt to solve: Simplifying 33 + -11n + n2 = 0 Solving 33 + -11n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -11n + -33 + n2 = 0 + -33 Reorder the terms: 33 + -33 + -11n + n2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -11n + n2 = 0 + -33 -11n + n2 = 0 + -33 Combine like terms: 0 + -33 = -33 -11n + n2 = -33 The n term is -11n. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11n + 30.25 + n2 = -33 + 30.25 Reorder the terms: 30.25 + -11n + n2 = -33 + 30.25 Combine like terms: -33 + 30.25 = -2.75 30.25 + -11n + n2 = -2.75 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = -2.75 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.Solution
n = {0}
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