How many solutions?

Algebra Level 1

Let x\left\lfloor x \right\rfloor denote the greatest integer less that or equal to xx.

So, Find the sum of all possible solutions of

x+2x+4x+8x+16x+32x=12345\left\lfloor x \right\rfloor+ \left\lfloor 2x \right\rfloor+\left\lfloor 4x \right\rfloor+\left\lfloor 8x \right\rfloor+\left\lfloor 16x \right\rfloor+\left\lfloor 32x \right\rfloor=12345

Note: If you feel that there are no such possible values of x, type the answer as 00


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