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Simplifying 2n2 + 18n = 580 * 2 Reorder the terms: 18n + 2n2 = 580 * 2 Multiply 580 * 2 18n + 2n2 = 1160 Solving 18n + 2n2 = 1160 Solving for variable 'n'. Reorder the terms: -1160 + 18n + 2n2 = 1160 + -1160 Combine like terms: 1160 + -1160 = 0 -1160 + 18n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-580 + 9n + n2) = 0 Factor a trinomial. 2((-29 + -1n)(20 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -1n)' equal to zero and attempt to solve: Simplifying -29 + -1n = 0 Solving -29 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + -1n = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -1n = 0 + 29 -1n = 0 + 29 Combine like terms: 0 + 29 = 29 -1n = 29 Divide each side by '-1'. n = -29 Simplifying n = -29Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve: Simplifying 20 + -1n = 0 Solving 20 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1n = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1n = 0 + -20 -1n = 0 + -20 Combine like terms: 0 + -20 = -20 -1n = -20 Divide each side by '-1'. n = 20 Simplifying n = 20Solution
n = {-29, 20}
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