Question 1066127
Let x be the smaller integer.

Then  {{{x*(x+9) = 360 }}}
       {{{ x^2 + 9x - 360 = 0 }}}
       {{{ (x+24)(x-15) = 0 }}}

{{{x=-24}}} or  {{{ x=15}}}

x=-24 —> x+9 = -15   

x=15 —> x+9 = 24
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Answers:
              1.  -24 and -15
    and
              2.   15 and 24
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Check:   1. -15 is 9 more than -24, and (-24)(-15) = 360  (ok)
             2.  24 is 9 more than 15, and (24)(15) = 360  (ok)