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Simplifying -4n2 + 10n + 41 = -9 Reorder the terms: 41 + 10n + -4n2 = -9 Solving 41 + 10n + -4n2 = -9 Solving for variable 'n'. Reorder the terms: 41 + 9 + 10n + -4n2 = -9 + 9 Combine like terms: 41 + 9 = 50 50 + 10n + -4n2 = -9 + 9 Combine like terms: -9 + 9 = 0 50 + 10n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 5n + -2n2) = 0 Factor a trinomial. 2((5 + -1n)(5 + 2n)) = 0 Ignore the factor 2.Subproblem 1
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 = 5Subproblem 2
Set the factor '(5 + 2n)' equal to zero and attempt to solve: Simplifying 5 + 2n = 0 Solving 5 + 2n = 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 + 2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2n = 0 + -5 2n = 0 + -5 Combine like terms: 0 + -5 = -5 2n = -5 Divide each side by '2'. n = -2.5 Simplifying n = -2.5Solution
n = {5, -2.5}
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