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^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.