Can you explain the “mathy” way to do problem 14 on Official Test 10? (I backsolved and got the correct answer, but I wondered if the “official” way to solve it was faster.)


You mean on the no calculator section, right?

The “official” way is slower here, for sure. That’s because, after you do all the math, you STILL NEED TO BACKSOLVE. When we do it the “official” way though, we call backsolving “checking for extraneous solutions.”


So there’s the math—it shows you that the possible solutions are 1 and 9 (which the answer choices already told you). From there, you need to put both back into the original equation to see which is extraneous.

\sqrt{4(1)}=(1)-3\\2=-2 <– that’s not true!

\sqrt{4(9)}=(9)-3\\6=6 <– that is true.

So there you have it: 9 works and 1 doesn’t.

Not to beat a dead horse here but if you do this the mathy way, you’re still doing exactly the same thing in the end that you’d have been doing in the beginning if you chose to backsolve. Backsolve won’t always be faster than the math, but for extraneous solution questions, it will be.

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