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Simplifying 2n2 = 7n + 9 Reorder the terms: 2n2 = 9 + 7n Solving 2n2 = 9 + 7n Solving for variable 'n'. Reorder the terms: -9 + -7n + 2n2 = 9 + 7n + -9 + -7n Reorder the terms: -9 + -7n + 2n2 = 9 + -9 + 7n + -7n Combine like terms: 9 + -9 = 0 -9 + -7n + 2n2 = 0 + 7n + -7n -9 + -7n + 2n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -9 + -7n + 2n2 = 0 Factor a trinomial. (-1 + -1n)(9 + -2n) = 0Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve: Simplifying -1 + -1n = 0 Solving -1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1n = 0 + 1 -1n = 0 + 1 Combine like terms: 0 + 1 = 1 -1n = 1 Divide each side by '-1'. n = -1 Simplifying n = -1Subproblem 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 = {-1, 4.5}
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