Don't mind the spelling mistake

Let $AC=2a$ and $CD=b$ . Then by the secant-tangent rule, ${4}^{2}=(2a+b)b$ . But ${x}^{2}={3}^{2}-{a}^{2}+{(a+b)}^{2}$ . Hence $x=5$ .

First of all BC is equal to BA that is 3cm according to secants rule. Then again with secant's theorem DC* DA=DE* DE=16. Lastly apply stewart's theorem in triangle ABD.