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Simplifying 4n2 + 400n + -630000 = 0 Reorder the terms: -630000 + 400n + 4n2 = 0 Solving -630000 + 400n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-157500 + 100n + n2) = 0 Factor a trinomial. 4((-450 + -1n)(350 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-450 + -1n)' equal to zero and attempt to solve: Simplifying -450 + -1n = 0 Solving -450 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + -1n = 0 + 450 Combine like terms: -450 + 450 = 0 0 + -1n = 0 + 450 -1n = 0 + 450 Combine like terms: 0 + 450 = 450 -1n = 450 Divide each side by '-1'. n = -450 Simplifying n = -450Subproblem 2
Set the factor '(350 + -1n)' equal to zero and attempt to solve: Simplifying 350 + -1n = 0 Solving 350 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + -1n = 0 + -350 Combine like terms: 350 + -350 = 0 0 + -1n = 0 + -350 -1n = 0 + -350 Combine like terms: 0 + -350 = -350 -1n = -350 Divide each side by '-1'. n = 350 Simplifying n = 350Solution
n = {-450, 350}
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