help geometry

https://ibb.co/JjhF45Q

Let angle BAD = 90º

BD = 5

AX = 2.4

BX = 1.8

DX = 3.2

CX = sqrt(CD² - DX²) 

BC = sqrt(BX² + CX²) = √29

Find length BC.

$\text{Let $BC = \color{red}x$}$

$\begin{array}{|lrcll|} \hline (1): & AE^2+DE^2 &=& 4^2 \\ (2): & DE^2+CE^2 &=& 6^2 \\ (3): & AE^2+BE^2 &=& 3^2 \\ (4): & BE^2+CE^2 &=& x^2 \\ \hline \end{array}$

$\small{ \begin{array}{|lrcll|} \hline (3)-(1)+(2): & (AE^2+BE^2)-(AE^2+DE^2)+ (DE^2+CE^2) &=& 3^2-4^2+6^2 \\ & BE^2+CE^2 &=& 3^2-4^2+6^2 \\ & BE^2+CE^2 &=& 29 \quad | \quad BE^2+CE^2 = x^2 \quad (4) \\ & x^2 &=& 29 \\ & \mathbf{x} &=& \mathbf{\sqrt{29}} \\ \hline \end{array} }$

$BC = \sqrt{29}$