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Simplifying 5n2 + -9n = 80 Reorder the terms: -9n + 5n2 = 80 Solving -9n + 5n2 = 80 Solving for variable 'n'. Reorder the terms: -80 + -9n + 5n2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -9n + 5n2 = 0 Factor a trinomial. (-16 + -5n)(5 + -1n) = 0Subproblem 1
Set the factor '(-16 + -5n)' equal to zero and attempt to solve: Simplifying -16 + -5n = 0 Solving -16 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -5n = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5n = 0 + 16 -5n = 0 + 16 Combine like terms: 0 + 16 = 16 -5n = 16 Divide each side by '-5'. n = -3.2 Simplifying n = -3.2Subproblem 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 = {-3.2, 5}
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