(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to solve 0 = 5x^{2}- 50x + 125 with solutions x = 5, x = 8.

2. Relevant equations

Referencing this thread I arrived at the equation (x - 5)(x - 8) = 5x^{2}- 50x + 125. Expanding

x^{2}- 13x + 40 = 5x^{2}- 50x + 125

3. The attempt at a solution

I tried to simply compare coefficients here but I saw that for x^{2}this would give me 1_{b}= 5_{10}which I don't think is possible. So what I did instead was factor out a 5 giving

x^{2}- 13x + 40 = 5(x^{2}- 10x + 25) which I set up the system

1_{b}= 1_{10}-> 1 = 1

-13_{b}= -10_{10}-> 1 * b + 3 = 10

40_{b}= 25_{10}-> 4 * b + 0 = 25

The first equation is not helpful at all, the second givers b = 7 which is not possible with x = 8 and the third gives b = 6.25 which is also not possible.

I'm really stumped here. Any help would be awesome.

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# Homework Help: Solve quadratic in non-10 base

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