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Simplifying 4n2 + -24n + -62 = 2 Reorder the terms: -62 + -24n + 4n2 = 2 Solving -62 + -24n + 4n2 = 2 Solving for variable 'n'. Reorder the terms: -62 + -2 + -24n + 4n2 = 2 + -2 Combine like terms: -62 + -2 = -64 -64 + -24n + 4n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -64 + -24n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-16 + -6n + n2) = 0 Factor a trinomial. 4((-2 + -1n)(8 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {-2, 8}
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