SOLUTION: The square of the greater of two consecutive even numbers exceeds the square of the smaller by 36. Find the numbers. Need with steps.. Please send fast.. Thanks

Question 628317: The square of the greater of two consecutive even numbers exceeds the square of the smaller by 36. Find the numbers.
Need with steps.. Please send fast.. Thanks
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First we must understand that consecutive even numbers are 2 apart from each other. So if the smaller one is x then the next one would be x+2. Or if the larger one is x then the next one down is x-2. Either of these pairs of expressions will work. I prefer to work with additions over subtractions so I'll go with the first pair:
Smaller even number: x
Next larger even number: x+2

Next we translate "The square of the greater of two consecutive even numbers exceeds the square of the smaller by 36" into a mathematical sentence (i.e. an equation).
"The square of the greater" translates into . Note the parentheses. Both the x and the 2 are part of the greater number. So if we square the greater number we have to square the whole thing, not just part of it. (If you're confused about when to use parentheses, then just use them all the time!)
"the square of the smaller" translates into

The "exceeds ... by 36" translates into +36
Translating the whole sentence we get:

We can now use this equation to solve the problem. First we simplify. Use FOIL on (x+2)(x+2) or use the pattern to multiply out the left side. I prefer using patterns:

which simplifies to:

Next we want the variable on just one side of the equation. Subtracting from each side:

With the squared terms canceling themselves out like they did, this equation has become a very easy one to solve. Subtracting f4 from each side we get:

Looking back we decided that
Smaller even number: x
and
Next larger even number: x+2
(This is why it is good to write these things down.) SO the solution to you problem are the values of x and x+2: 8 and 8+2 or 10.
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