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Simplifying 2n2 = 36 + n Solving 2n2 = 36 + n Solving for variable 'n'. Reorder the terms: -36 + -1n + 2n2 = 36 + n + -36 + -1n Reorder the terms: -36 + -1n + 2n2 = 36 + -36 + n + -1n Combine like terms: 36 + -36 = 0 -36 + -1n + 2n2 = 0 + n + -1n -36 + -1n + 2n2 = n + -1n Combine like terms: n + -1n = 0 -36 + -1n + 2n2 = 0 Factor a trinomial. (-4 + -1n)(9 + -2n) = 0Subproblem 1
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 = -4Subproblem 2
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 = 4.5Solution
n = {-4, 4.5}
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