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Home / This expands to \( n^2 + n^2 + 2n + 1 = 85 \).

This expands to \( n^2 + n^2 + 2n + 1 = 85 \).

February 22, 2026

$This expands to \( n^2 + n^2 + 2n + 1 = 85 \).$

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Set each factor to zero: \( x-2 = 0 \) or \( x-3 = 0 \).
The solutions are \( x = 2 \) and \( x = 3 \).
The equation is \( n^2 + (n+1)^2 = 85 \).
Combine like terms: \( 2n^2 + 2n + 1 = 85 \).
Subtract 85: \( 2n^2 + 2n - 84 = 0 \).
Factor: \( (n-6)(n+7) = 0 \).

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