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Simplifying n(n + 2) = 675 Reorder the terms: n(2 + n) = 675 (2 * n + n * n) = 675 (2n + n2) = 675 Solving 2n + n2 = 675 Solving for variable 'n'. Reorder the terms: -675 + 2n + n2 = 675 + -675 Combine like terms: 675 + -675 = 0 -675 + 2n + n2 = 0 Factor a trinomial. (-27 + -1n)(25 + -1n) = 0Subproblem 1
Set the factor '(-27 + -1n)' equal to zero and attempt to solve: Simplifying -27 + -1n = 0 Solving -27 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + -1n = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -1n = 0 + 27 -1n = 0 + 27 Combine like terms: 0 + 27 = 27 -1n = 27 Divide each side by '-1'. n = -27 Simplifying n = -27Subproblem 2
Set the factor '(25 + -1n)' equal to zero and attempt to solve: Simplifying 25 + -1n = 0 Solving 25 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1n = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1n = 0 + -25 -1n = 0 + -25 Combine like terms: 0 + -25 = -25 -1n = -25 Divide each side by '-1'. n = 25 Simplifying n = 25Solution
n = {-27, 25}
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