isabelcelestine366 isabelcelestine366

04-10-2021
Mathematics

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Given that 221 base x =25 base 10..find the base of x

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LammettHash LammettHash

04-10-2021

If [tex]221_x=25_{10}[/tex], then

[tex]2x^2 + 2x + 1 = 25[/tex]

Solve for x :

[tex]2x^2+2x-24=0 \\\\ x^2 + x - 12 = 0 \\\\ (x+4)(x-3) = 0 \\\\ \boxed{x = -4 \text{ or }x=3}[/tex]

(Yes, bases can be negative.)

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