Answer
$z=2.27,5.73$
Work Step by Step
$z^2-8z=-13$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-8$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-8)^2}{4}=16$
To complete the square, add $\dfrac{49}{4}$ on both sides.
$z^2-8z+16=-13+16$
$\implies (z-4)^2=3$
$\implies (z-4)=1.73$
and
$\implies (z-4)=-1.73$
or, $z=2.27,5.73$
