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Simplifying 4n2 + 20n + -200 = 0 Reorder the terms: -200 + 20n + 4n2 = 0 Solving -200 + 20n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + 5n + n2) = 0 Factor a trinomial. 4((-10 + -1n)(5 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve: Simplifying -10 + -1n = 0 Solving -10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1n = 0 + 10 -1n = 0 + 10 Combine like terms: 0 + 10 = 10 -1n = 10 Divide each side by '-1'. n = -10 Simplifying n = -10Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-10, 5}
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