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Simplifying 16n2 + -116n = -14 + -2n Reorder the terms: -116n + 16n2 = -14 + -2n Solving -116n + 16n2 = -14 + -2n Solving for variable 'n'. Reorder the terms: 14 + -116n + 2n + 16n2 = -14 + -2n + 14 + 2n Combine like terms: -116n + 2n = -114n 14 + -114n + 16n2 = -14 + -2n + 14 + 2n Reorder the terms: 14 + -114n + 16n2 = -14 + 14 + -2n + 2n Combine like terms: -14 + 14 = 0 14 + -114n + 16n2 = 0 + -2n + 2n 14 + -114n + 16n2 = -2n + 2n Combine like terms: -2n + 2n = 0 14 + -114n + 16n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -57n + 8n2) = 0 Factor a trinomial. 2((1 + -8n)(7 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -8n)' equal to zero and attempt to solve: Simplifying 1 + -8n = 0 Solving 1 + -8n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -8n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8n = 0 + -1 -8n = 0 + -1 Combine like terms: 0 + -1 = -1 -8n = -1 Divide each side by '-8'. n = 0.125 Simplifying n = 0.125Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {0.125, 7}
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