Floor Floor Floor Floor

Algebra Level 5

Given the equation

xxxx=41 x \lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor = 41

If α\alpha denote the largest negative value of xx which satisfy the equation above, while β\beta denote the smallest positive value of xx which satisfy the equation above.

What is the value of 17α+28β17\alpha + 28\beta ?

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