SOLUTION: Please help me solve the following: Three consecutive even integers are such that the third number squared increased by the product of the other two numbers is 184. Find the numb

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Question 999558: Please help me solve the following:
Three consecutive even integers are such that the third number squared increased by the product of the other two numbers is 184. Find the numbers.
I tried this but it's not checking.
Let x= first even integer
x+2= second even integer
x+4= third even integer
(x+4)^2 +x(x+2)=184
(x+4)^2 +x(x+2)-184=0
x^2+8x+16+x^2+2x-184=0
2x^2+10x-168=0
x^2+5x-84=0
(x+12)(x-7)=0
x+12=0 x=-12
x-7=0 x=7
Answer by josgarithmetic(39621) (Show Source):
You can put this solution on YOUR website!
You should completely retry what you did, but start THIS WAY for your numbers:

x can be any integer.
2x will then be the first of your consecutive EVEN integers. The next two are 2x+2 and 2x+4.

Now your consecutive EVEN integers are:

Solve the problem now, according to those expressions.

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Upon rechecking your original work, the steps are still correct, regardless of the "x" or the "2x". The step which is WILL give what you need. The assumption was that x could be one of the even numbers.

Zero-Product Rule says that either x+12=0, leading directly to x=-12, or that x-7=0, leading directly to x=7. You KNOW that x=7 cannot be acceptable because this is ODD, and your description and question specified finding consecutive EVEN integers. You must then accept the result.

You know the rest. Either way, test the results.