Answer
$z=19,-17$
Work Step by Step
$z^2-2z=323$
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.
$z^2-2z+1=323+1$
$\implies (z-1)^2=324$
$\implies (z-1)=18$
and
$\implies (z-1)=-18$
or, $z=19,-17$
