The principal square root of a real number can't be negative. That's a little different than saying that the Cubs probably won't win the pennant next year. (Hey, we're just being realistic.)

Whatever 9x + 3 is, its square root definitely can't be -11. This equation has no real number solutions.

Example 2

Solve: .

The radical is all by itself on one side of the equation, so we can square both sides:

After rearranging, we can rewrite this equation as:

0 = x^{2} + x + 5

Then we can solve it using the quadratic formula. The solutions are:

Now we have a problem, because we can't take the square root of -19. This equation has no solutions. Foiled again.