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Simplifying 2n2 + -4n + 4 = 74 Reorder the terms: 4 + -4n + 2n2 = 74 Solving 4 + -4n + 2n2 = 74 Solving for variable 'n'. Reorder the terms: 4 + -74 + -4n + 2n2 = 74 + -74 Combine like terms: 4 + -74 = -70 -70 + -4n + 2n2 = 74 + -74 Combine like terms: 74 + -74 = 0 -70 + -4n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + -2n + n2) = 0 Factor a trinomial. 2((-5 + -1n)(7 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5Subproblem 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 = {-5, 7}
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