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## Homework Statement

The solution of the quadratic equation x

^{2}- 11x + 22 = 0 are x = 3 or x = 6. What is the base of the numbers?

## Homework Equations

Knowledge of how to convert from a generic base to decimal?

## The Attempt at a Solution

I tried to just place r in where I would have a value of s*r

^{1}

(x-3)(x-6) = x

^{2}- 11x + 22

x

^{2}- 6x - 3x + [1*r + 8] = x

^{2}- [x( r + 1)] + 2r + 1

r + 8 - 9x = x + 2r - xr + 1

7 - 10x = r(1-x)

r = (7-10x)/(1-x)

when I try to put either of the values of x in I get r as either 10.6 or 11.5

Please help me.