1.

Let the integers be 3 and -6

x^{2}+3x-18=0

If the signs are switched

The numbers are -3 and 6

x^{2}-3x-18=0

x(x+5) =24

Right hand side is not zero but 24

So we cannot write x=24 or x+5 =24

X^{2}+5x-24=0

X^{2}+8x-3x-24=0

X(x+8)-39X=8)=0

(x+8)(x-3)=0

Since RHS = 0, we can write

X= -8 or x =3

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