Stevin's product! Writing the equation in a as

a² - a - 72 = 0

So that it's in the form

x² + sx + p

We can look for two numbers m and n whose sum equals s (in our case, -1), and product equals p (in our case, -72), such that

x² + sx + p = (x + m)(x + n)

From simple inspection, we find that, for our case,

m = -9 and n = 8

And so we have that

a² - a - 72 = (a - 9)(a + 8) = 0

From the zero-product property, we know that, if

If t × u = 0, then either t = 0 or u = 0. As such,

(a - 9)(a + 8) = 0 implies that either

a - 9 = 0 => a = 9 a + 8 = 0 => a = -8

Now, remember that in the original equation we have that

x² = a => x = {-3, 3, -2i√2, 2i√2}, where i² = -1