The number of integral solutions of x^2+...

The number of integral solutions of `x^2+9<(x+3)^2<8x+25` is

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`x^2+9< (x+3)^2`
`x^2+9 `6x>0`
`x>0`
`x^2+9+6x<8x+25`
`x^2-2x-16<0`
`x=(2+-sqrt(4+64))/2`
`x=(2+-sqrt(17))/2`
...

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