Can you help me find the integers?

Question

The product of two consecutive even integers is 224. Find the integers.

Answer 1

First integer is x

Second integer is (x+2)

 

x(x+2) = 224

x² + 2x = 224

x² + 2x - 224 = 0

 

(x + 16)(x - 14) = 224

 

the first integer is either -16 or 14

One pair of answers is -16 and -14 which are consecutive, even, and have a product of 224.

The other possible pair of answers is 14 and 16, consecutive even numbers with a product of 224.

Answer 2

First even  number= x

 

second even number= x+2

 

(x)(x+2)=224

 

x²+2x=224

 

x²+2x-224=0

 

(x+16)(x-14)=0

 

x=-16   or x=14

 

So when x= 14  ,   x+2= 14+2= 16   so 2 consecutive even integers are 14 and 16

 

or

 

when x=-16  , x+2=-14     So consecutive even integers are -14 and -16