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Simplifying 5n2 = 48 + n Solving 5n2 = 48 + n Solving for variable 'n'. Reorder the terms: -48 + -1n + 5n2 = 48 + n + -48 + -1n Reorder the terms: -48 + -1n + 5n2 = 48 + -48 + n + -1n Combine like terms: 48 + -48 = 0 -48 + -1n + 5n2 = 0 + n + -1n -48 + -1n + 5n2 = n + -1n Combine like terms: n + -1n = 0 -48 + -1n + 5n2 = 0 Factor a trinomial. (-3 + -1n)(16 + -5n) = 0Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
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 = 3.2Solution
n = {-3, 3.2}
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