SOLUTION: What equation represents the product of two consecutives even intergers that equal 224?

Question 125795: What equation represents the product of two consecutives even intergers that equal 224?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If x represents the first of the consecutive integers, then the next consecutive integer must
be +2 greater than that or (x + 2).
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Therefore, the equation you are looking for is:
.
x*(x + 2) = 224
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When you multiply this out you get:
.

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and by subtracting 224 from both sides this results in:
.

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This form of the equation is in the standard form of a quadratic equation. It can be solved
by factoring or, if you prefer, by applying the quadratic formula.
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If you apply either of those methods you should find that the two possible answers for
x are x = 14 and x = -16.
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Therefore the possible solutions for this problem (two consecutive even numbers whose product
equals 224 are
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First pair 14 and 16
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Second pair -16 and -14
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As you can see, both pairs are consecutive even integers, and if you multiply the members
of each of these sets of pairs you get 224. Therefore, they check as being the correct
answers to the problem.
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Hope this helps you to understand the problem and work your way through it.
.

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