Solve: a^2-14 a-51 - Vidyadip

Question

Solve:
$a^2-14 a-51$

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Answer

$a^2-14 a-51$
$=a^2-14 a+\left(\frac{14}{2}\right)^2-\left(\frac{14}{2}\right)^2-51\left[\text { Adding and subtracting }\left(\frac{14}{2}\right)^2, \text { that is } 7^2\right]$
$=a^2-14 a+7^2-7^2-51$
$=(a-7)^2-100[\text { comleting the square }]$
$=(a-7)^2-10^2$
$=[(a-7)-10][(a-7)+10]$
$=(a-7-10)(a-7+10)$
$=(a-17)(a+3)$

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