Factorize each of the following quadratic polynomials by using the method of completing the square:

$a^{2}-14 a-51$

$=a^{2}-14 a+\left(\frac{14}{2}\right)^{2}-\left(\frac{14}{2}\right)^{2}-51 \quad\left[\right.$ Adding and subtracting $\left(\frac{14}{2}\right)^{2}$, that is, $\left.7^{2}\right]$

$=a^{2}-14 a+7^{2}-7^{2}-51$

$=(a-7)^{2}-100 \quad[$ Completing the square $]$

$=(a-7)^{2}-10^{2}$

$=[(a-7)-10][(a-7)+10]$

$=(a-7-10)(a-7+10)$

$=(a-17)(a+3)$