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Simplifying 10n2 + -28n + 22 = 6 Reorder the terms: 22 + -28n + 10n2 = 6 Solving 22 + -28n + 10n2 = 6 Solving for variable 'n'. Reorder the terms: 22 + -6 + -28n + 10n2 = 6 + -6 Combine like terms: 22 + -6 = 16 16 + -28n + 10n2 = 6 + -6 Combine like terms: 6 + -6 = 0 16 + -28n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -14n + 5n2) = 0 Factor a trinomial. 2((4 + -5n)(2 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -5n)' equal to zero and attempt to solve: Simplifying 4 + -5n = 0 Solving 4 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5n = 0 + -4 -5n = 0 + -4 Combine like terms: 0 + -4 = -4 -5n = -4 Divide each side by '-5'. n = 0.8 Simplifying n = 0.8Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {0.8, 2}
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