The product of two consecutive even integers is 624. How do you find the integers?

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Answer 1 · 2018-06-18T12:15:20

See a solution process below:

First, let's call the first number: #x#

Then the next consecutive even integer would be: #x + 2#

Therefore their product in standard form would be:

#x(x + 2) = 624#

#x^2 + 2x = 624#

#x^2 + 2x - color(red)(624) = 624 - color(red)(624)#

#x^2 + 2x - 624 = 0#

We can factor this as:

(x + 26)(x - 24) = 0

Now, we can solve each term on the left side of the equation for #0#:

Solution 1:

#x + 26 = 0#

#x + 26 - color(red)(26) = 0 - color(red)(26)#

#x + 0 = -26#

#x = -26#

Solution 2:

#x - 24 = 0#

#x - 24 + color(red)(24) = 0 + color(red)(24)#

#x - 0 = 24#

#x = 24#

If the first number is #-26# then the second number is:

#-26 + 2 = -24#

#-26 * -24 = 624#

If the first number is 24 then the second number is:

#24 + 2 = 26#

#24 * 26 = 624#

There are two solutions to this problem:

#{-26, -24}#; #{24, 26}#