SOLUTION: two consecutive numbers are squared and then added to gether to get the result of 113. What is the starting formula?

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Question 451604: two consecutive numbers are squared and then added to gether to get the result of 113. What is the starting formula?
Found 3 solutions by nerdybill, Alan3354, pedjajov:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
two consecutive numbers are squared and then added to gether to get the result of 113. What is the starting formula?
.
Let x = first consecutive number
then
x+1 = second consecutive number
.
x^2 + (x+1)^2 = 113 (you can probably leave it like this)
x^2 + (x+1)(x+1) = 113
x^2 + (x^2+x+x+1) = 113
x^2 + (x^2+2x+1) = 113
2x^2+2x+1 = 113

Answer by Alan3354(69443) About Me  (Show Source):
Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
Two consecutive numbers are x and x+1 so if their sum is 113 it is

x%5E2+%2B+%28x%2B1%29%5E2+=+113
x%5E2+%2B+x%5E2+%2B+2x+%2B+1+=+113
2x%5E2+%2B+2x+-+112+=0
Solutions for x in this quadratic equation are given as

x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A2%2A%28-112%29+%29%29%2F%282%2A2%29+

It gives us x = 7 or x = -8
So numbers are 7 and 8, or -8 and -7.

Check1: 7%5E2%2B8%5E2=+49+%2B+64+=+113, OK
Check2: %28-8%29%5E2+%2B+%28-7%29%5E2+=+64+%2B+49+=+113, OK