Question 113275
Consecutive even integers follow the form: {{{2x}}}, {{{2x+2}}}, etc



So when they say "The product of two consecutive positive even integers is 360", they mean symbolically:


{{{(2x)(2x+2)=360}}}



{{{4x^2+4x=360}}} Distribute



{{{4x^2+4x-360=0}}} Subtract 360 from both sides



{{{4(x^2+x-90)=0}}} Factor {{{4x^2+4x-360}}}




{{{4(x+10)(x-9)=0}}} Factor {{{x^2+x-90}}} (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:


{{{x+10=0}}} or {{{x-9=0}}}


{{{x=-10}}} or {{{x=9}}}  Now solve for x in each case



So our solutions are {{{x=-10}}} or {{{x=9}}}



However, since it is stated that the integers must be positive, {{{x=9}}} is the only solution



Now plug {{{x=9}}} into {{{2x}}} to find the 1st number:


{{{2(9)=18}}}


So our 1st number is 18





Now plug {{{x=9}}} into {{{2x+2}}} to find the 2nd number:


{{{2(9)+2=18+2=20}}}


So our 2nd number is 20




So our two numbers are 18 and 20



Check:


When we multiply 18 and 20, we should get 360


{{{18*20=360}}}



{{{360=360}}} Since we do, our answer is verified.