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Simplifying 2n2 + n + -46 = -10 Reorder the terms: -46 + n + 2n2 = -10 Solving -46 + n + 2n2 = -10 Solving for variable 'n'. Reorder the terms: -46 + 10 + n + 2n2 = -10 + 10 Combine like terms: -46 + 10 = -36 -36 + n + 2n2 = -10 + 10 Combine like terms: -10 + 10 = 0 -36 + n + 2n2 = 0 Factor a trinomial. (-9 + -2n)(4 + -1n) = 0Subproblem 1
Set the factor '(-9 + -2n)' equal to zero and attempt to solve: Simplifying -9 + -2n = 0 Solving -9 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2n = 0 + 9 -2n = 0 + 9 Combine like terms: 0 + 9 = 9 -2n = 9 Divide each side by '-2'. n = -4.5 Simplifying n = -4.5Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-4.5, 4}
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