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Simplifying n2 = 30 + n Solving n2 = 30 + n Solving for variable 'n'. Reorder the terms: -30 + -1n + n2 = 30 + n + -30 + -1n Reorder the terms: -30 + -1n + n2 = 30 + -30 + n + -1n Combine like terms: 30 + -30 = 0 -30 + -1n + n2 = 0 + n + -1n -30 + -1n + n2 = n + -1n Combine like terms: n + -1n = 0 -30 + -1n + n2 = 0 Factor a trinomial. (-5 + -1n)(6 + -1n) = 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 '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-5, 6}
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