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Simplifying 8n2 = -64 + 72n Solving 8n2 = -64 + 72n Solving for variable 'n'. Reorder the terms: 64 + -72n + 8n2 = -64 + 72n + 64 + -72n Reorder the terms: 64 + -72n + 8n2 = -64 + 64 + 72n + -72n Combine like terms: -64 + 64 = 0 64 + -72n + 8n2 = 0 + 72n + -72n 64 + -72n + 8n2 = 72n + -72n Combine like terms: 72n + -72n = 0 64 + -72n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(8 + -9n + n2) = 0 Factor a trinomial. 8((1 + -1n)(8 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 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 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {1, 8}
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