Question 329890
Look for solutions that look like,
{{{x^2+x-n=(x+a)(x+b)=0}}} where a and b are integers.
Using the FOIL method,
{{{x^2+x-n=x^2+(a+b)x+ab}}}
Comparing,
1.{{{a+b=1}}}
2.{{{ab=-n}}}
From eq. 1,
{{{b=1-a}}}
Substituting into eq. 2,
{{{a(1-a)=-n}}}
{{{highlight(n=a(a-1))}}} where a is any integer.
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Two examples:
{{{a=0}}},{{{b=1}}},{{{n=0}}}
{{{x^2+x=x(x+1)=0}}} 
solutions:{{{x=-a=0}}},{{{x=-b=-1}}}
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{{{a=5}}},{{{b=-4}}},{{{n=5(4)=20}}}
{{{x^2+x-20=(x+5)(x-4)}}}
solutions:{{{x=-a=-5}}},{{{x=-b=4}}}
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