Let's solve the quadratic equations one by one, factor them, and then match the solutions to the table provided to complete the code. I'll go through each equation and provide the solutions.

1. $x^2 + x - 6 = 0$

Factor the quadratic: $x^2 + x - 6 = (x - 2)(x + 3) = 0$ The solutions are: $x = 2 \quad \text{or} \quad x = -3$ From the table, $2$ corresponds to R and $-3$ corresponds to D.

2. $x^2 + 3x + 2 = 0$

Factor the quadratic: $x^2 + 3x + 2 = (x + 1)(x + 2) = 0$ The solutions are: $x = -1 \quad \text{or} \quad x = -2$ From the table, $-1$ corresponds to I and $-2$ corresponds to H.

3. $x^2 - x - 6 = 0$

Factor the quadratic: $x^2 - x - 6 = (x - 3)(x + 2) = 0$ The solutions are: $x = 3 \quad \text{or} \quad x = -2$ From the table, $3$ corresponds to F and $-2$ corresponds to H.

4. $x^2 - 3x + 2 = 0$

Factor the quadratic: $x^2 - 3x + 2 = (x - 1)(x - 2) = 0$ The solutions are: $x = 1 \quad \text{or} \quad x = 2$ From the table, $1$ corresponds to G and $2$ corresponds to R.

5. $x^2 + 5x + 6 = 0$

Factor the quadratic: $x^2 + 5x + 6 = (x + 2)(x + 3) = 0$ The solutions are: $x = -2 \quad \text{or} \quad x = -3$ From the table, $-2$ corresponds to H and $-3$ corresponds to D.

6. $x^2 - 7x + 12 = 0$

Factor the quadratic: $x^2 - 7x + 12 = (x - 3)(x - 4) = 0$ The solutions are: $x = 3 \quad \text{or} \quad x = 4$ From the table, $3$ corresponds to F and $4$ corresponds to E.

7. $x^2 - 4x + 3 = 0$

Factor the quadratic: $x^2 - 4x + 3 = (x - 1)(x - 3) = 0$ The solutions are: $x = 1 \quad \text{or} \quad x = 3$ From the table, $1$ corresponds to G and $3$ corresponds to F.

8. $x^2 - 9x + 18 = 0$

Factor the quadratic: $x^2 - 9x + 18 = (x - 3)(x - 6) = 0$ The solutions are: $x = 3 \quad \text{or} \quad x = 6$ From the table, $3$ corresponds to F and $6$ corresponds to Q.

9. $x^2 + x - 56 = 0$

Factor the quadratic: $x^2 + x - 56 = (x - 7)(x + 8) = 0$ The solutions are: $x = 7 \quad \text{or} \quad x = -8$ From the table, $7$ corresponds to S and $-8$ corresponds to V.

10. $x^2 + 2x - 35 = 0$

Factor the quadratic: $x^2 + 2x - 35 = (x - 5)(x + 7) = 0$ The solutions are: $x = 5 \quad \text{or} \quad x = -7$ From the table, $5$ corresponds to K and $-7$ corresponds to T.

11. $x^2 - 6x - 27 = 0$

Factor the quadratic: $x^2 - 6x - 27 = (x - 9)(x + 3) = 0$ The solutions are: $x = 9 \quad \text{or} \quad x = -3$ From the table, $9$ corresponds to O and $-3$ corresponds to D.

To complete the code at the bottom of the page, we need to use these results and the corresponding letters from the table.

Do you want me to help you fill in the boxes and verify the final code?