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Simplifying 8n2 = 224 + -24n Solving 8n2 = 224 + -24n Solving for variable 'n'. Reorder the terms: -224 + 24n + 8n2 = 224 + -24n + -224 + 24n Reorder the terms: -224 + 24n + 8n2 = 224 + -224 + -24n + 24n Combine like terms: 224 + -224 = 0 -224 + 24n + 8n2 = 0 + -24n + 24n -224 + 24n + 8n2 = -24n + 24n Combine like terms: -24n + 24n = 0 -224 + 24n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-28 + 3n + n2) = 0 Factor a trinomial. 8((-7 + -1n)(4 + -1n)) = 0 Ignore the factor 8.Subproblem 1
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 = -7Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 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 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-7, 4}
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