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Simplifying 2 + 8n + 4n * n + -191842 = 0 Multiply n * n 2 + 8n + 4n2 + -191842 = 0 Reorder the terms: 2 + -191842 + 8n + 4n2 = 0 Combine like terms: 2 + -191842 = -191840 -191840 + 8n + 4n2 = 0 Solving -191840 + 8n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-47960 + 2n + n2) = 0 Factor a trinomial. 4((-220 + -1n)(218 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-220 + -1n)' equal to zero and attempt to solve: Simplifying -220 + -1n = 0 Solving -220 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '220' to each side of the equation. -220 + 220 + -1n = 0 + 220 Combine like terms: -220 + 220 = 0 0 + -1n = 0 + 220 -1n = 0 + 220 Combine like terms: 0 + 220 = 220 -1n = 220 Divide each side by '-1'. n = -220 Simplifying n = -220Subproblem 2
Set the factor '(218 + -1n)' equal to zero and attempt to solve: Simplifying 218 + -1n = 0 Solving 218 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-218' to each side of the equation. 218 + -218 + -1n = 0 + -218 Combine like terms: 218 + -218 = 0 0 + -1n = 0 + -218 -1n = 0 + -218 Combine like terms: 0 + -218 = -218 -1n = -218 Divide each side by '-1'. n = 218 Simplifying n = 218Solution
n = {-220, 218}
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