Question 460277
Let x be the number Thomas is thinking of

{{{(2x-5) * (x+3) = 13}}}
 Multiply the left side to give
{{{2x^2+6x-5x-15 =13}}}

{{{2x^2 +x-15 =13 }}}
(divide both sides by 2.)

{{{x^2+(x/2)-(15/2) = (13/2)}}}


{{{x^2+(x/2) = (13/2) + (15/2) = (28/2) = 14}}}


{{{(x+(1/4))^2) - (1/16) = 14}}}


{{{(x+(1/4))^2)  = 14+ (1/16) = 225/16}}}


{{{x+(1/4)  =  (225/16)^(1/2)}}}



{{{x+(1/4) = (15/4)}}}
  Or
{{{x+(1/4) = -(15/4)}}}

So

{{{x = 3.5}}} Or {{{x=-4}}}