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Simplifying 4n3 + -44n2 + 122n = 0 Reorder the terms: 122n + -44n2 + 4n3 = 0 Solving 122n + -44n2 + 4n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(61 + -22n + 2n2) = 0 Ignore the factor 2.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 '(61 + -22n + 2n2)' equal to zero and attempt to solve: Simplifying 61 + -22n + 2n2 = 0 Solving 61 + -22n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 30.5 + -11n + n2 = 0 Move the constant term to the right: Add '-30.5' to each side of the equation. 30.5 + -11n + -30.5 + n2 = 0 + -30.5 Reorder the terms: 30.5 + -30.5 + -11n + n2 = 0 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + -11n + n2 = 0 + -30.5 -11n + n2 = 0 + -30.5 Combine like terms: 0 + -30.5 = -30.5 -11n + n2 = -30.5 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 = -30.5 + 30.25 Reorder the terms: 30.25 + -11n + n2 = -30.5 + 30.25 Combine like terms: -30.5 + 30.25 = -0.25 30.25 + -11n + n2 = -0.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = -0.25 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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