SOLUTION: Hello. Here is my question. I know how to solve this problem if it didn't have the second square root in front of the "x" on the left of the equality. I would show you work but all

Algebra ->  Radicals -> SOLUTION: Hello. Here is my question. I know how to solve this problem if it didn't have the second square root in front of the "x" on the left of the equality. I would show you work but all      Log On


   

Question 32069: Hello. Here is my question. I know how to solve this problem if it didn't have the second square root in front of the "x" on the left of the equality. I would show you work but all I have been able to do is move the -1 over to the left side (as a +1). After that, I can't do anything else until I get rid of the squareroot in front of the "x". Here is the problem: +sqrt%28x%29=+sqrt%28+x%2B2+%29-1+.
Thank you for any help you can provide.
-Chris
Found 2 solutions by Cintchr, stanbon:
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%28x%29=+sqrt%28+x%2B2+%29-1+
I, too, would move the 1 to the left first.
+sqrt%28x%29%2B1=+sqrt%28x%2B2%29+
Square both sides
+%28sqrt%28x%29%2B1%29%5E2=+%28sqrt%28x%2B2%29%29%5E2+
on the right, the square cancels the root
+%28sqrt%28x%29%2B1%29%5E2+=x%2B2+
+%28sqrt%28x%29%2B1%29%28sqrt%28x%29%2B1%29=x%2B2+
Foil the left side
F : +sqrt%28x%29+%2A+sqrt%28x%29+=+x+
O : +sqrt%28x%29+%2A+1+=+sqrt%28x%29+
I : +1+%2A+sqrt%28x%29+=+sqrt%28x%29+
L : +1+%2A+1+=+1+
Bring it all together
+x+%2B+2%28sqrt%28x%29%29%2B+1=x%2B2+
Move the x and the 1 to the right by subtracting
+2%28sqrt%28x%29%29=+1+
divide by 2
+sqrt%28x%29=+1%2F2+
square both sides again
+%28sqrt%28x%29%29%5E2=+%281%2F2%29%5E2+
+x+=+1%2F4+
Plug the 1/4 into the original equation to check
+sqrt%28x%29=+sqrt%28+x%2B2+%29-1+
+sqrt%281%2F4%29=+sqrt%28+%281%2F4%29%2B2+%29-1+
+sqrt%281%2F4%29=+sqrt%289%2F4%29-1+
+1%2F2+=+%283%2F2%29+-1+
+1%2F2+=+1%2F2+
YES!!!
So x does equal 1/4

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
sqrtx-sqrt(x+2)=-1
Square both sides to get:
[x-2(sqrtx(x+2))+x+2=1
Simplify:
2x+2-2sqrt[x^2+2x]=1
Rewrite as follows:
2sqrt[x^2+2x]=2x+1
Square both sides to get:
4(x^2+2x]=4x^2+4x+1
8x=4x+1
4x=1
x=1/4
Check that answer in the original equation.
It works.
Cheers,
Stan H.