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Simplifying 2n2 = 7n + -5 Reorder the terms: 2n2 = -5 + 7n Solving 2n2 = -5 + 7n Solving for variable 'n'. Reorder the terms: 5 + -7n + 2n2 = -5 + 7n + 5 + -7n Reorder the terms: 5 + -7n + 2n2 = -5 + 5 + 7n + -7n Combine like terms: -5 + 5 = 0 5 + -7n + 2n2 = 0 + 7n + -7n 5 + -7n + 2n2 = 7n + -7n Combine like terms: 7n + -7n = 0 5 + -7n + 2n2 = 0 Factor a trinomial. (1 + -1n)(5 + -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 '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5Solution
n = {1, 2.5}
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