Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference.

To complete the polynomial equation, we need to subtract the second expression from the first and ensure that the resulting difference matches the third expression.

Let's set up the expression:

1st polynomial: \( 9x^2 + bx + 13 \)

2nd polynomial: \( -2x^2 + 12x + c \)

3rd polynomial (result): \( dx^2 + 5x + 2 \)

Accordingly, we will subtract the second polynomial from the first:

\[
(9x^2 + bx + 13) - (-2x^2 + 12x + c) = (9x^2 + bx + 13) + (2x^2 - 12x - c)
\]

Now, let's combine like terms:

\[
(9x^2 + 2x^2) + (bx - 12x) + (13 - c) = (9 + 2)x^2 + (b - 12)x + (13 - c)
\]

This leads to:

\[
11x^2 + (b - 12)x + (13 - c)
\]

We want the resulting polynomial to match:

\[
dx^2 + 5x + 2
\]

Comparing coefficients, we get the following equations:

1. \( d = 11 \)
2. \( b - 12 = 5 \)
3. \( 13 - c = 2 \)

From \( d = 11 \), we have \( d = 11 \).

From \( b - 12 = 5 \):
\[
b = 5 + 12 = 17
\]

From \( 13 - c = 2 \):
\[
c = 13 - 2 = 11
\]

So, we can fill in the blanks with:
- For \( bx \): \( 17x \)
- For \( c \): \( 11 \)

Thus, the completed polynomial equation is:

\[
9x^2 + 17x + 13
\]
\[
- ( -2x^2 + 12x + 11)
\]
\[
= 11x^2 + 5x + 2
\]

So the filled polynomial is:

\( 9x^2 + 17x + 13 \)
\( -2x^2 + 12x + 11 \)
\( 11x^2 + 5x + 2 \)