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Simplifying -2n2 + -16n + -90 = -10n2 Reorder the terms: -90 + -16n + -2n2 = -10n2 Solving -90 + -16n + -2n2 = -10n2 Solving for variable 'n'. Combine like terms: -2n2 + 10n2 = 8n2 -90 + -16n + 8n2 = -10n2 + 10n2 Combine like terms: -10n2 + 10n2 = 0 -90 + -16n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -8n + 4n2) = 0 Factor a trinomial. 2((-5 + -2n)(9 + -2n)) = 0 Ignore the factor 2.Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(9 + -2n)' equal to zero and attempt to solve: Simplifying 9 + -2n = 0 Solving 9 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2n = 0 + -9 -2n = 0 + -9 Combine like terms: 0 + -9 = -9 -2n = -9 Divide each side by '-2'. n = 4.5 Simplifying n = 4.5Solution
n = {-2.5, 4.5}
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