Extracting the Root

TheKeyboardist

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Aug 30, 2005
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Basically, what i had to do in this section was to solve for x. After a couple pages, i ran into some problems. My first difficulty was:

1/2(x+7)^2=8

Steps:

1. 1/2(x^2+49)=8
2. (x^2+49)=16
3. x^2=-33
4. x=(square root of)-33
5. x=(sq. rt of)-11 * (sq. rt of)3

I cant figure this one out! Please tell me what went wrong in my steps. Or if i can simplify any further.

There was one other:

3/5(x-1/2)^2=4

I pretty much simplified it the same was as before and got to x=(sq. rt of) 924/12 which i further simplified to 2(sq rt)3*(sq rt)11*(sq rt)7. Im having the same trouble here! Thanks in advance!!!
 
Well, thanks for that tip but i dont exactly know what to do with that. If i try to take it to the next step, i get stuck with the x^2. Thanks for helping though!
 
You say that you can't find the correct answer (from the solution manual, or the back of your text?). What is the correct answer?

Eliz.
 
Stapel, what are you talking about? This was a question in my practice packet and i dont know how to solve it. There is no answer key, its just a packet of questions. And i dont know the correct answer so im asking for help.
 
Well, it should work with the corection but the simplest way is to <u>not</u> expand (x+7)
(x+7)2=16
x+7=<u>+</u>4
Now that you know the answers you should be able to apply the quardatic quation to
x²+14x+49=16
x²+14x+33=0
Or use whatever method you know. It factors nicely.
 
thanks for that gene! So the answer would be x=-11!

But sadly, i dont think i can apply that to 3/5(x-1/2)^2=4.

So what should i do about that one?
 
That's half the answer. That is a plus or minus 4. You used the -4. Use the plus 4 too.
You can use the same method on the other, but it isn't as friendly.
(x-.5)^2=20/3=60/9=4*15/9
x-.5= <u>+</u> (2/3)sqrt(15)
 
Im really sorry for being such a bother but i really dont know what to do. I tried what i did in the last step. I tested both negative and positive.

So it became

x= (2/3)sqrt(15)+1/2 and
x-=-(2/3)sqrt(15)+1/2

I plugged both in the original equation but what i got didnt equal 4.
 
That's odd. It works for me. The plus answer goes
((2/3)sqrt(15)+.5-.5)² =
4*15/9 =
20/3
(3/5)*(20/3)=4
 
ohh, i see my mistake, i multiplied 1/4 instead of 4/1. Alright, thanks for your time, thanks everybody! Im finally done my packet just in time for school!
 
Hmmm...are you sure that's not: 1/2(x-7)^2=8 instead of 1/2(x+7)^2=8
?

Then nice and round:
x^2 - 14x + 49 = 16
x^2 - 14x + 33 = 0
(x - 11)(x - 3) = 0
 
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