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Simplifying 24n8 + -27n6 + 21n4 = 0 Reorder the terms: 21n4 + -27n6 + 24n8 = 0 Solving 21n4 + -27n6 + 24n8 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n4'. 3n4(7 + -9n2 + 8n4) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n4' equal to zero and attempt to solve: Simplifying n4 = 0 Solving n4 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n4 = 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 '(7 + -9n2 + 8n4)' equal to zero and attempt to solve: Simplifying 7 + -9n2 + 8n4 = 0 Solving 7 + -9n2 + 8n4 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + -1.125n2 + n4 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -1.125n2 + -0.875 + n4 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -1.125n2 + n4 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -1.125n2 + n4 = 0 + -0.875 -1.125n2 + n4 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -1.125n2 + n4 = -0.875 The n term is -1.125n2. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125n2 + 0.31640625 + n4 = -0.875 + 0.31640625 Reorder the terms: 0.31640625 + -1.125n2 + n4 = -0.875 + 0.31640625 Combine like terms: -0.875 + 0.31640625 = -0.55859375 0.31640625 + -1.125n2 + n4 = -0.55859375 Factor a perfect square on the left side: (n2 + -0.5625)(n2 + -0.5625) = -0.55859375 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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