Thomas R. answered • 04/24/18

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Over 25 years of experience and a sense of humor about math

I am guessing you meant:

X - 1 = √ (7-X) Okay, these can be verysneaky because even when you finish, one or more answers could be lies.

Still, the idea is simple enough. Get one of the radicals alone (you only have one, so that is easy,

but if you had more than one, just pick whichever you like), then square both sides:

(X-1)

^{2}= (√(7-X) )^{2}You have to FOIL out the left side...(X-1)(X-1) = 7 - X but the right side escapes its radical.

X

^{2}- 2X + 1 = 7 - X Ahhhh, I see a polynomial, so we have to drag everything to one side and get zero on the other: +X - 7 -7 +X

X

^{2}- X - 6 = 0 Luckily, this one comes in peace and wants to be factored:(X - 3)(X + 2) = 0 Set each to zero using the Zero Factor Property (creative name, huh?)

X - 3=0 X + 2=0 then solve:

X = 3 X = -2 ....or are they? You must

**always**plug both answers into the original equation to see if they work.Typically, when they do not both work. you get something like " 5 = -5" or "-2 = 2", which means you can't keep that answer.You will find at least one of the answers we got falls into that category.