Question

Think of a number, double the number,

Answer 1

Answer:

Let x be the number

double x = 2 x

square the result  (2x)^2

(2x)^2 - x     subtract the original number

4 x^2 - x = 33

4 x^2 - x - 33 = 0

Solve the quadratic

(1 +- (1 + 4 * 132)^1/2) / 8

= (1 + 528^1/2) / 8 = (1 + 23) / 8   = 3    using the positive exponent

Check:

(2 * 3)^2 - 3 = 36 - 3 = 33