gentle mortar
Hello math enthusiasts:
In the problem from 6:09 to 10:50 in this Chad's prep video:
https://www.youtube.com/watch?v=xU3kUaRng9I
Chad tells us if the x value in (x)(x+.1) is less than 5% of .1 you can just ignore the x in that parenthesis because it makes a negligible contribution to the final result. My question is, how do you know the value of x before solving the problem in order to somewhat-accurately infer if it's more/less than 5% of the number its being added/subtracted to?
The common method of checking if the K value is very small (I'm afraid a little chemistry background is needed to answer my question) and using that to estimate the value of x has actually gotten me the wrong answer on a previous homework, partially because the question-maker was being cheeky and gave me an x-value just a tiny bit above 5% of the number it's added/subtracted to, so even though the K value was very small the quadratic formula needed to be used to get the correct answer.
Is there any other more accurate shortcut of estimating the value of x to high accuracy or is using the quadratic formula really the only safe option every time? Thank you.
rugged rock