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Simplifying 2N2 + -2N + 1 = 265 Reorder the terms: 1 + -2N + 2N2 = 265 Solving 1 + -2N + 2N2 = 265 Solving for variable 'N'. Reorder the terms: 1 + -265 + -2N + 2N2 = 265 + -265 Combine like terms: 1 + -265 = -264 -264 + -2N + 2N2 = 265 + -265 Combine like terms: 265 + -265 = 0 -264 + -2N + 2N2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-132 + -1N + N2) = 0 Factor a trinomial. 2((-11 + -1N)(12 + -1N)) = 0 Ignore the factor 2.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 '(12 + -1N)' equal to zero and attempt to solve: Simplifying 12 + -1N = 0 Solving 12 + -1N = 0 Move all terms containing N to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1N = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1N = 0 + -12 -1N = 0 + -12 Combine like terms: 0 + -12 = -12 -1N = -12 Divide each side by '-1'. N = 12 Simplifying N = 12Solution
N = {-11, 12}
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