could someone help me comprehend this equation?

Question

The product of two consecutive even integers is 80. Find the two integers. Answer in the form of paired points with the lowest of the two integers first.

 

(________ ,  ________) or (_________ , ________)

Answer 1

Hi Jared.

 

If you have consecutive even integers whose values you don't know, you can call your first integer "x" and your second integer will be "x+2". This is because consecutive even integers are always spaced out by 2 (think 2 and 4, 12 and 14, 56 and 58, etc).

 

You know that the product of your consecutive even integers is 80.

 

So

 

x*(x+2) = 80

 

x^2 + 2x = 80

 

x^2 + 2x - 80 = 0

 

(x + 10)(x - 8) = 0

 

x = -10

x = 8

 

So your first even integer is either -10 or 8.

 

If your first even integer is -10, that means your second even integer is -8.

 

If your first even integer is 8, your second even integer is 10.

 

(-10, -8), (8, 10)

 

Hope this helps.