SOLUTION: Please help me with this question!!! I have NO CLUE what i am doing!! Here is the question: The sum of the squares of two consecutive negative even integers is 100. Find the intege

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Please help me with this question!!! I have NO CLUE what i am doing!! Here is the question: The sum of the squares of two consecutive negative even integers is 100. Find the intege      Log On


   

Question 23418: Please help me with this question!!! I have NO CLUE what i am doing!! Here is the question: The sum of the squares of two consecutive negative even integers is 100. Find the integers.
Please help me, help would be greatly appreciated.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start by letting x = the first negative even integer. The next consecutive negative even integer is x+2.
From the problem description, you can write:
x%5E2+%2B+%28x%2B2%29%5E2+=+100 Simplify and solve for x.
x%5E2+%2B+x%5E2+%2B+4x+%2B+4+=+100 Subtract 100 from both sides of the equation.
2x%5E2+%2B+4x+-+96+=+0 Factor out a 2.
2%28x%5E2+%2B+2x+-+48%29+=+0 Factor the parentheses.
2%28x+-+6%29%28x+%2B+8%29+=+0 Apply the zero product principle.
x+-+6+=+0 and/or x+%2B+8+=+0
If x+-+6+=+0 then x+=+6 Discard this solution...you want negative integers.
If x+%2B+8+=+0 then x+=+-8 This solution is valid and x%2B2+=+-8%2B2 = -6
The two consecutive negative even integers are:
-8 and -6
Check:
%28-8%29%5E2+%2B+%28-6%29%5E2+=+64+%2B+36 = 100