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Simplifying n3 + 8n2 + 25n = 0 Reorder the terms: 25n + 8n2 + n3 = 0 Solving 25n + 8n2 + n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(25 + 8n + n2) = 0Subproblem 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 '(25 + 8n + n2)' equal to zero and attempt to solve: Simplifying 25 + 8n + n2 = 0 Solving 25 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 8n + -25 + n2 = 0 + -25 Reorder the terms: 25 + -25 + 8n + n2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 8n + n2 = 0 + -25 8n + n2 = 0 + -25 Combine like terms: 0 + -25 = -25 8n + n2 = -25 The n term is 8n. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8n + 16 + n2 = -25 + 16 Reorder the terms: 16 + 8n + n2 = -25 + 16 Combine like terms: -25 + 16 = -9 16 + 8n + n2 = -9 Factor a perfect square on the left side: (n + 4)(n + 4) = -9 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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