document.write( "Question 129550: If [x] represents the greatest integer less than or equal to x, Solve for [x]: x * [x] = 40 \n" ); document.write( "

Algebra.Com's Answer #94603 by ilana(307) $\"\"$ $\"About$

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I just used guess and check. I got [x]=6. First, I pretended x was an integer, because then [x]=x. Start with x=1. If x=1, x=1. If x=2, x=4. Continue until x=6: x=36, x=7: x=49. So this [x] must be somewhere around 6 or 7. If x is between 5 and 6, then x=5._*5, which is less than 6*5=30, so that's not it. If x is between 6 and 7, then x=6._*6, which is bigger than 6*6=36 but less than 7*6=42, so that works. So we didn't find out the exact x, but [x]=6. You can see that is the only value that works because in order for [x] to be 7, x would need to be greater than or equal to 7, so x would be greater than or equal to 49, much too big. \n" ); document.write( "

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