How do you use approximation instead of the Quadratic Formula?

Question

In this exmaple: x^2 / (0.0550-x) = 2.13 x 10^-11

How would I use approximation method instead of using the quadratic formula?? I know that we assume that x is small and we set up...

x^2 / (0.550)= 2.13 x 10^-11

Solving for X= 1.17 x 10^-12 whenI plug this back in it does not equal 2.13 x 10^-11.... so where do I go from here??

Answer 1

First, you're not following your own music. You dropped a "zero" from the denominator.
What you are solving is x^2 = 1.17x10^-12, from which x= 1.08x10^-6. This should work.
Note the approximation is that x<<0.0550, which looks OK.

Answer 2

when the constant is less than one, such as yours, you can assume that x is going to account for less than a 5% difference in the reaction. This is known as the "5% Rule" You did it correctly