Question 79073
Let x=the integer

Now we are told that {{{x+x^2=12}}}  subtract 12 from both sides


{{{x^2+x-12=0}}}  quadratic in standard form and it can be factored.  The factors are:

{{{(x+4)(x-3)=0}}}

Remember, when the A coefficient of a quadratic is 1, then the B coefficient will be the sum of the factors of the C coefficient, if the quadratic is factorable.

x=-4-----------------------one answer

and

x=3---------------------------another answer

CK  
-4+(-4)^2=12
-4+16=12
12=12

Now for 3

3+(3)^2=12
3+9=12
12=12

Hope this helps---ptaylor