To find the value of \( x \), we first need to understand the relationship between angles \( \angle ABD \) and \( \angle CBD \). Assuming that points A, B, C, and D are positioned such that angles \( ABD \) and \( CBD \) are adjacent and form a linear pair (meaning they are supplementary), we can write the equation:
\[ \angle ABD + \angle CBD = 180^\circ \]
Substituting the expressions for the angles, we get:
\[ (0.19x + 58) + (0.06x + 37) = 180 \]
Now, we can combine like terms:
\[ 0.19x + 0.06x + 58 + 37 = 180 \]
This simplifies to:
\[ 0.25x + 95 = 180 \]
Next, we isolate \( x \) by subtracting 95 from both sides:
\[ 0.25x = 180 - 95 \]
\[ 0.25x = 85 \]
Now, divide both sides by 0.25 to solve for \( x \):
\[ x = \frac{85}{0.25} \]
\[ x = 340 \]
Thus, the value of \( x \) is:
\[ \boxed{340} \]