I need help solving for x.​

x= 9

Step-by-step explanation:

Please see the attached picture.

In △BCD

∠BDC= 180° -90° (adj. ∠s on a str. line)

∠BDC= 90°

Applying Pythagoras' Theorem,

(BD)² +(DC)²= (BC)²

(BC)²= 6² +4²

(BC)²= 52 -----(1)

In △ABD

Applying Pythagoras' Theorem,

(AD)² +(BD)²= (AB)²

(AB)²= x² +6²

(AB)²= x² +36 -----(2)

In △ABC

Applying Pythagoras' Theorem,

(AB)² +(BC)²= (AC)²

(AB)² +(BC)²= (x +4)²

Substitute (1) and (2):

x² +36 +52= (x +4)²

x² +88= x² +2(x)(4) +4² (simplify, expand)

x² +88= x² +8x +16

8x +16= 88 (-x² on both sides)

8x= 88 -16

8x= 72

x= 72 ÷8

x= 9

207/8 is the right