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Simplifying 25n2 + 80 = 120n Reorder the terms: 80 + 25n2 = 120n Solving 80 + 25n2 = 120n Solving for variable 'n'. Reorder the terms: 80 + -120n + 25n2 = 120n + -120n Combine like terms: 120n + -120n = 0 80 + -120n + 25n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(16 + -24n + 5n2) = 0 Factor a trinomial. 5((4 + -5n)(4 + -1n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + -5n)' equal to zero and attempt to solve: Simplifying 4 + -5n = 0 Solving 4 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5n = 0 + -4 -5n = 0 + -4 Combine like terms: 0 + -4 = -4 -5n = -4 Divide each side by '-5'. n = 0.8 Simplifying n = 0.8Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {0.8, 4}
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