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Simplifying 2n2 + 5n = 117 Reorder the terms: 5n + 2n2 = 117 Solving 5n + 2n2 = 117 Solving for variable 'n'. Reorder the terms: -117 + 5n + 2n2 = 117 + -117 Combine like terms: 117 + -117 = 0 -117 + 5n + 2n2 = 0 Factor a trinomial. (-9 + -1n)(13 + -2n) = 0Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve: Simplifying -9 + -1n = 0 Solving -9 + -1n = 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 + -1n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n = 0 + 9 -1n = 0 + 9 Combine like terms: 0 + 9 = 9 -1n = 9 Divide each side by '-1'. n = -9 Simplifying n = -9Subproblem 2
Set the factor '(13 + -2n)' equal to zero and attempt to solve: Simplifying 13 + -2n = 0 Solving 13 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2n = 0 + -13 -2n = 0 + -13 Combine like terms: 0 + -13 = -13 -2n = -13 Divide each side by '-2'. n = 6.5 Simplifying n = 6.5Solution
n = {-9, 6.5}
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