SOLUTION: Okay, well I am in Agebra 2. I have never really understood the concepts, as much as I try. I take all notes in the class, and how they come up with these numbers, I have no clue.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Okay, well I am in Agebra 2. I have never really understood the concepts, as much as I try. I take all notes in the class, and how they come up with these numbers, I have no clue.       Log On


   

Question 29563: Okay, well I am in Agebra 2. I have never really understood the concepts, as much as I try. I take all notes in the class, and how they come up with these numbers, I have no clue.
I guess one of the biggest problems I am having are the "extraneous solutions".
I don't like the answers givien to me, but I do like knowing how to do them and the steps... ONe of them problems is
The square root of x +12 = x.
From what I understood from my teacher.. I waould trop the x+12 down like
x + 12 = x
-x -x
12 ? Square root of 12 =3.50??
What did I do wrong?
Another problem is
(3x-8)^1/2=5
3x-8^1/2 =5 I dropped the 3x-8
+8 +8 I added 8 to both sides
3x^1/2=13 and I don't know what to do? Divide by three? Then if I do that? what happesn to the the power?
Any help of what I am doing wrong, would be greatly appreciated.
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not quite sure about what the first problem is asking. Try rewriting it with the parenthesis or symbols to clarify it. I'll try to answer the second one instead.
Starting with %283x-8%29%5E%281%2F2%29=5 You can't just drop the parenthesis... they have meaning. To rewrite without them as 3x-8%5E%281%2F2%29=5 would change the problem. Instead, as we solve virtually every algebra equation, we have to do the same thing to both sides. Since we're first concerned with the 1/2 exponent outside the parentesis on the right, we can get rid of it by squaring both sides:
%28%283x-8%29%5E%281%2F2%29%29%5E2=5%5E2The rule here being that by to eliminate the exponent (1/2) you want to raise the exponent to the recipical (2/1=2). When you take an exponent and raise it to another exponent, you multiply the two together. In brief: %28x%5Ea%29%5Eb=x%5E%28a%2Ab%29 So in our example 1/2*2=1 so we end up with:
3x-8=25Now this should look like something familiar and you can solve by adding 8 to both sides:
3x=33Divide by 3:
x=11
Double checking:
%283x-8%29%5E%281%2F2%29=5
%283%2811%29-8%29%5E%281%2F2%29=5
%2833-8%29%5E%281%2F2%29=5
%2825%29%5E%281%2F2%29=5Check.