Math - Quadratic Equations

Two consecutive even numbers have a product of 288. What are the numbers?

The answer I got through trial and error was 18 and 16. Is there a way for me to form the question into an equation and work that out to find the answer, instead of just guessing numbers? Thanks.

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  1. what do you know about even numbers? They differ by 2, right?

    So, if the smaller number is x, then the larger one is x+2

    x(x+2) = 288

    now solve that.

    Or, if you consider u as the number between the two even ones, then

    (u-1)(u+1) = u^2-1 = 288
    u^2 = 289
    u=17
    so the numbers are 16 and 18.

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