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Simplifying 648n5 + -512n = 0 Reorder the terms: -512n + 648n5 = 0 Solving -512n + 648n5 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8n'. 8n(-64 + 81n4) = 0 Factor a difference between two squares. 8n((8 + 9n2)(-8 + 9n2)) = 0 Ignore the factor 8.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 '(8 + 9n2)' equal to zero and attempt to solve: Simplifying 8 + 9n2 = 0 Solving 8 + 9n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 9n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 9n2 = 0 + -8 9n2 = 0 + -8 Combine like terms: 0 + -8 = -8 9n2 = -8 Divide each side by '9'. n2 = -0.8888888889 Simplifying n2 = -0.8888888889 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-8 + 9n2)' equal to zero and attempt to solve: Simplifying -8 + 9n2 = 0 Solving -8 + 9n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 9n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 9n2 = 0 + 8 9n2 = 0 + 8 Combine like terms: 0 + 8 = 8 9n2 = 8 Divide each side by '9'. n2 = 0.8888888889 Simplifying n2 = 0.8888888889 Take the square root of each side: n = {-0.942809042, 0.942809042}Solution
n = {0, -0.942809042, 0.942809042}
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