Given that 356_x = BC₁₆. Find the value of x.

Change BC in base 16 to base 10. B = 11 and C = 12, so 11 × 16 + 12 = 188.

Now write 356 in base x: 3x² + 5x + 6 = 188, so 3x² + 5x − 182 = 0.

Test x = 7: 3(49) + 35 + 6 = 147 + 35 + 6 = 188. It works, so x = 7.

(Factorised: (3x + 26)(x − 7) = 0, and the base must be positive.)