The product of two consecutive even intergers is 80. Find the two intergers

Question

The product of a two consecutive even integers is 80 find the two integers.

Answer 1

Let one integer is x.

Then it's consecutive even integer would be x+2.

Product of the integers x(x+2) = 80

x^2+2x = 80

Subtract 80 from each side.

x^2+2x-80 = 0

x^2+10x-8x-80 = 0

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

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

x+10 = 0

Subtract 10 from each side.

x = -10

and x-8 = 0

Add 8 to each side.

x = 8

If x = -10 then integers are -10,-8.

If x = 8 then integers are 10,8.