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Simplifying 5n2 = 5 + -24n Solving 5n2 = 5 + -24n Solving for variable 'n'. Reorder the terms: -5 + 24n + 5n2 = 5 + -24n + -5 + 24n Reorder the terms: -5 + 24n + 5n2 = 5 + -5 + -24n + 24n Combine like terms: 5 + -5 = 0 -5 + 24n + 5n2 = 0 + -24n + 24n -5 + 24n + 5n2 = -24n + 24n Combine like terms: -24n + 24n = 0 -5 + 24n + 5n2 = 0 Factor a trinomial. (-5 + -1n)(1 + -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 '(1 + -5n)' equal to zero and attempt to solve: Simplifying 1 + -5n = 0 Solving 1 + -5n = 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 + -5n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5n = 0 + -1 -5n = 0 + -1 Combine like terms: 0 + -1 = -1 -5n = -1 Divide each side by '-5'. n = 0.2 Simplifying n = 0.2Solution
n = {-5, 0.2}
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