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To find the total area of both flowers and vegetables combined, we need to add the two given expressions together.
The areas are:
1. Area of flower beds: \( 3x^2 + 5x - 2 \)
2. Area of vegetable plants: \( 2x^2 - 3x + 4 \)
Now, let's add these two expressions together:
\[
(3x^2 + 5x - 2) + (2x^2 - 3x + 4)
\]
Now, we combine like terms:
1. Combine the \( x^2 \) terms:
\[
3x^2 + 2x^2 = 5x^2
\]
2. Combine the \( x \) terms:
\[
5x - 3x = 2x
\]
3. Combine the constant terms:
\[
-2 + 4 = 2
\]
Putting it all together, we get:
\[
5x^2 + 2x + 2
\]
Thus, the total area of both flowers and vegetables combined is:
\[
\boxed{5x^2 + 2x + 2} \text{ square feet.}
\]