The mean proportional between $(x - 2)$ and $(x + 7)$ is 6. If x is positive, what is x?

Explanation

1. 01

   $(x - 2)(x + 7) = 6^2 = 36$.

2. 02

   $x^2 + 5x - 14 = 36$, so $x^2 + 5x - 50 = 0$.

3. 03

   $(x + 10)(x - 5) = 0$, so $x = 5$ (x must be positive).

4. 04

   Check: the numbers are 3 and 12, and √$(3 \times 12) = 6$.