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Simplifying 2n2 = 35 + 3n Solving 2n2 = 35 + 3n Solving for variable 'n'. Reorder the terms: -35 + -3n + 2n2 = 35 + 3n + -35 + -3n Reorder the terms: -35 + -3n + 2n2 = 35 + -35 + 3n + -3n Combine like terms: 35 + -35 = 0 -35 + -3n + 2n2 = 0 + 3n + -3n -35 + -3n + 2n2 = 3n + -3n Combine like terms: 3n + -3n = 0 -35 + -3n + 2n2 = 0 Factor a trinomial. (-7 + -2n)(5 + -1n) = 0Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve: Simplifying -7 + -2n = 0 Solving -7 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2n = 0 + 7 -2n = 0 + 7 Combine like terms: 0 + 7 = 7 -2n = 7 Divide each side by '-2'. n = -3.5 Simplifying n = -3.5Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-3.5, 5}
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