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Simplifying 5n2 + 17n + -48 = -8 Reorder the terms: -48 + 17n + 5n2 = -8 Solving -48 + 17n + 5n2 = -8 Solving for variable 'n'. Reorder the terms: -48 + 8 + 17n + 5n2 = -8 + 8 Combine like terms: -48 + 8 = -40 -40 + 17n + 5n2 = -8 + 8 Combine like terms: -8 + 8 = 0 -40 + 17n + 5n2 = 0 Factor a trinomial. (-5 + -1n)(8 + -5n) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(8 + -5n)' equal to zero and attempt to solve: Simplifying 8 + -5n = 0 Solving 8 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5n = 0 + -8 -5n = 0 + -8 Combine like terms: 0 + -8 = -8 -5n = -8 Divide each side by '-5'. n = 1.6 Simplifying n = 1.6Solution
n = {-5, 1.6}
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