SOLUTION: find two consecutive positive intergers such that the square of the larger integer added to seven times the smaller integer is equal to 253?

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Question 370490: find two consecutive positive intergers such that the square of the larger integer added to seven times the smaller integer is equal to 253?
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
Let x & (x+1) be the 2 integers.
(x+1)^2+7x=253
x^2+2x+1+7x=253
x^2+9x+1-253=0
x^2+9x-252=0
(x-12)(x+21)=0
x-12=0
x=12 ANS FOR THE SMALLER INTEGER.
12+1=13 ANS. FOR THE LARGER INTEGER.
Proof:
13^2+7*12=253
169+84=253
253=253