Hello llse,

First you need to define your variables. Think of what consecutive even numbers would be......

2, 4, 6,..... 10,12,14,16.... Etc.

what if I started with x?

well it takes +2 to get to the next number, so the variables I need are:

x: the first positive even integer

x+2 : the second positive integer

Secondly, I need to "interpret" the English word *product* to the math operation MULTIPLICATION.

this means my equation is

x(x+2) =624

x^2 +2x =624 distribute the x to both factors in the parentheses

x^2 +2x -624=624-624. Move all parts to one side of the equation

x^2 +2x -624=0. Simplify, now factor because it is a squared equation

(x-24)(x+26)=0 two numbers that equal 624when multiplied but 2 when added together

x-24=0. And x+26=0. Set each factor equal to zero and solve

x=24. And x=-26. Simplify

x+2=26. and x+2=-24. Finding the second even integer

But wait, the problem wants POSITIVE even integers so 2 of the solutions DO NOT work (-26,-24, they are negative) be careful sometimes you get extraneous ("extra") solutions, look at your defined variables.

the solutions we want are 24 and 26.