Question
Solve:
$a^2- 14a - 51$
$a^2- 14a - 51$
✓
Answer
$a^2- 14a - 51$
$=\text{a}^2-14\text{a}+\Big(\frac{14}{2}\Big)^2-\Big(\frac{14}{2}\Big)^2-51$ $\Big[$Adding and subtracting $\Big(\frac{14}{2}\Big)^2,$ that is $7^2\Big]$
$ =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)$
$=\text{a}^2-14\text{a}+\Big(\frac{14}{2}\Big)^2-\Big(\frac{14}{2}\Big)^2-51$ $\Big[$Adding and subtracting $\Big(\frac{14}{2}\Big)^2,$ that is $7^2\Big]$
$ =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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