Whenever you have to square both sides to solve, you have to check for extraneous solutions.
![image](https://i0.wp.com/78.media.tumblr.com/c38fbefe43c6d98a3f74af0d1b7485fb/tumblr_inline_pdea69hn7p1qio24w_540.png?w=852&ssl=1)
That tells you m could be 2 or –10, but because part of the solution was squaring both sides, you need to run both possible solutions through the original equation.Try 2 first:
![image](https://i0.wp.com/78.media.tumblr.com/2822f071f4bf398b1764d2b7573a50e0/tumblr_inline_pdea9tJXRm1qio24w_540.png?w=852&ssl=1)
That works, now how about –10?
![image](https://i0.wp.com/78.media.tumblr.com/01fae7114426ba3cbd3933607e5223d9/tumblr_inline_pdeafs9GiL1qio24w_540.png?w=852&ssl=1)
Nope. Remember that the square root function √ returns only positive results, so –10 is an extraneous solution that doesn’t work in the original equation. The sum of all solutions is just 2.
One more note here: I often think it’s worth graphing questions like this.
![](https://i0.wp.com/78.media.tumblr.com/926009f174a495a812915ad851b11918/tumblr_inline_pdeapzfLvg1qio24w_540.png?w=852&ssl=1)
It should be obvious from that graph that there’s only one intersection of the two functions, at x = 2.
from Tumblr https://ift.tt/2B5QuHh