Question 222390
How do i solve by factoring,{{{x^2-13x+40=0}}}


Step 1.  Find two integers m and n whose sum {{{m+n=-13}}} and whose product is {{{mn=40}}}


Step 2.  After trial and error, the integers are m=-5 and n=-8.


Step 3.  Then using these integers we have {{{x^2-13x+40=(x-5)(x-8)=0}}}


Step 4.  We have two solutions, {{{x-5=0}}} and {{{x-8=0}}} or {{{x=5}}} and {{{x=8}}}.


Step 5.  ANSWER:  The answer is  {{{x=5}}} and {{{x=8}}}.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J