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Home » x^2 + 2x - 3 = 8 - Silent Sales Machine

x^2 + 2x - 3 = 8 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📝 Recent Posts

The sum of the first \( n \) terms of an arithmetic sequence is given...
The sum formula: \( S_n = rac{n}{2} (2a + (n-1)d) \)
Set equal: \( rac{n}{2} (2a + (n-1)d) = 3n^2 + 5n \)
Divide both sides by \( n \) (for \( n
\( rac{1}{2} (2a + (n-1)d) = 3n + 5 \)
\( 2a + (n-1)d = 6n + 10 \)
Expand left: \( 2a + dn - d = dn + (2a - d) \)
So: \( dn + (2a - d) = 6n + 10 \)
\( d = 6 \)
\( 2a - d = 10 \Rightarrow 2a - 6 = 10 \Rightarrow 2a = 16 \Rightarrow...

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