Answer
$a=7,-5$
Work Step by Step
$a^2-2a-35=0$
or, $a^2-2a=35$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-2$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-2)^2}{4}=1$
To complete the square, add $1$ on both sides.
$a^2-2a+1=35+1$
$\implies (a-1)^2=36$
$\implies (a-1)=6$
and
$\implies (a-1)=-6$
or, $a=7,-5$
