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Simplifying -64n4 + 24n2 = 0 Reorder the terms: 24n2 + -64n4 = 0 Solving 24n2 + -64n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8n2'. 8n2(3 + -8n2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}Subproblem 2
Set the factor '(3 + -8n2)' equal to zero and attempt to solve: Simplifying 3 + -8n2 = 0 Solving 3 + -8n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8n2 = 0 + -3 -8n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8n2 = -3 Divide each side by '-8'. n2 = 0.375 Simplifying n2 = 0.375 Take the square root of each side: n = {-0.612372436, 0.612372436}Solution
n = {0, -0.612372436, 0.612372436}
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