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Simplifying n(7n + 28) = 539 Reorder the terms: n(28 + 7n) = 539 (28 * n + 7n * n) = 539 (28n + 7n2) = 539 Solving 28n + 7n2 = 539 Solving for variable 'n'. Reorder the terms: -539 + 28n + 7n2 = 539 + -539 Combine like terms: 539 + -539 = 0 -539 + 28n + 7n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-77 + 4n + n2) = 0 Factor a trinomial. 7((-11 + -1n)(7 + -1n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-11 + -1n)' equal to zero and attempt to solve: Simplifying -11 + -1n = 0 Solving -11 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1n = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1n = 0 + 11 -1n = 0 + 11 Combine like terms: 0 + 11 = 11 -1n = 11 Divide each side by '-1'. n = -11 Simplifying n = -11Subproblem 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 = {-11, 7}
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