To solve the equation \( x^2 \cdot x + 3 = 19 \), we first simplify it. The equation can be rewritten as:
\[ x^3 + 3 = 19 \]
Now, subtract 3 from both sides:
\[ x^3 = 16 \]
Next, take the cube root of both sides:
\[ x = \sqrt[3]{16} \]
The cube root of 16 can be simplified, but it is not a perfect cube, so we can calculate a numerical approximation:
\[ x \approx 2.52 \]
Thus, the solution to the equation \( x^2 \cdot x + 3 = 19 \) is:
\[ x = \sqrt[3]{16} \approx 2.52 \]