Product of two consecutive even integers

Question

Product of two consecutive even integers is 528. Find the integers. (Positive and negative)

Answer 1

x and x+2 are the integers

x(x+2)=528

x^2+2x=528

x^2+2x-528=0

factor 528

528=2*2*2*2*3*11

rearrange the factors

(2*2*2*3)*(2*11)=24*22 and 24-22=2, the coefficient of the second term

factor

(x+24)(x-22)=0

x+24=0

x=-24 and x+2=-22

x-22=0

x=22 and x+2=24

you have two solutions (done algebraically)

 

a simpler arithmetic solution is √528=22.978...

now use 22 and 24

22 and 22+2=24 are the solutions, along with the negatives

 

in reality all you have to do is factor 528 into a product of primes like I did before and group the factors accordingly

this is what the algebra all comes down to