SOLUTION: Can you help me with this problem? Find two consecutive positive even integers whose sum of their squares is 6500.

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Question 755522: Can you help me with this problem? Find two consecutive positive even integers whose sum of their squares is 6500.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + (x+2)^2 = 6500

x^2 + x^2 + 4x + 4 = 6500

2x^2 + 4x + 4 = 6500

2x^2 + 4x + 4 - 6500 = 0

2x^2 + 4x - 6496 = 0


Use the quadratic formula to solve for x

x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%284%29%2B-sqrt%28%284%29%5E2-4%282%29%28-6496%29%29%29%2F%282%282%29%29 Plug in a+=+2, b+=+4, c+=+-6496

x+=+%28-4%2B-sqrt%2816-%28-51968%29%29%29%2F%284%29

x+=+%28-4%2B-sqrt%2816%2B51968%29%29%2F%284%29

x+=+%28-4%2B-sqrt%2851984%29%29%2F4

x+=+%28-4%2Bsqrt%2851984%29%29%2F4 or x+=+%28-4-sqrt%2851984%29%29%2F4

x+=+%28-4%2B228%29%2F4 or x+=+%28-4-228%29%2F4

x+=+224%2F4 or x+=+-232%2F4

x+=+56 or x+=+-58

x = 56

x + 2 = 56 + 2 = 58

So the two consecutive positive even integers are 56 and 58.