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Simplifying 3n2(9n + -1n3 + 8n5) = 0 (9n * 3n2 + -1n3 * 3n2 + 8n5 * 3n2) = 0 (27n3 + -3n5 + 24n7) = 0 Solving 27n3 + -3n5 + 24n7 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n3'. 3n3(9 + -1n2 + 8n4) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n3' equal to zero and attempt to solve: Simplifying n3 = 0 Solving n3 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n3 = 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 '(9 + -1n2 + 8n4)' equal to zero and attempt to solve: Simplifying 9 + -1n2 + 8n4 = 0 Solving 9 + -1n2 + 8n4 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -0.125n2 + n4 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -0.125n2 + -1.125 + n4 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -0.125n2 + n4 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -0.125n2 + n4 = 0 + -1.125 -0.125n2 + n4 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -0.125n2 + n4 = -1.125 The n term is -0.125n2. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125n2 + 0.00390625 + n4 = -1.125 + 0.00390625 Reorder the terms: 0.00390625 + -0.125n2 + n4 = -1.125 + 0.00390625 Combine like terms: -1.125 + 0.00390625 = -1.12109375 0.00390625 + -0.125n2 + n4 = -1.12109375 Factor a perfect square on the left side: (n2 + -0.0625)(n2 + -0.0625) = -1.12109375 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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