## Greatest Integer X

If [X] represents the greatest integer function, then [X] represents the greatest integer less than or equal to X.  Find the value of X if the product of X and [X] equals 200.
Source: mathcontest.olemiss.edu 1/112010

SOLUTION
If $X=14.25$, then $14.25\times [14.25]=14.25\times 14=199.5$.

If $X=14.30$, then $14.30\times [14.30]=14.30\times 14=200.2$.

Let $X=200\div 14=14.28571429$, then
$14.28571429\times [14.28571429]=14.28571429\times 14=200$.

Answer: $X=14.28571429$.