SOLUTION: Solve the radical equation. sqrt(3x+4)=2+ sqrt(x) This will usually involve squaring each side twice. I don't know how to resolve this, can you please give an explanation as

Algebra ->  Radicals -> SOLUTION: Solve the radical equation. sqrt(3x+4)=2+ sqrt(x) This will usually involve squaring each side twice. I don't know how to resolve this, can you please give an explanation as       Log On


   

Question 737647: Solve the radical equation. sqrt(3x+4)=2+ sqrt(x)
This will usually involve squaring each side twice.
I don't know how to resolve this, can you please give an explanation as to how to perform this?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Given: sqrt%283x%2B4%29=2%2B+sqrt%28x%29

Square both sides.
3x%2B4=4%2B4sqrt%28x%29%2Bx

Operate to get just the irrational on one side and everything else on the other.
Also simplify.
3x=4sqrt%28x%29%2Bx
3x-x=4sqrt%28x%29
2x=4sqrt%28x%29
x=2sqrt%28x%29
Square both sides.
x%5E2=4%2Ax

A little more to get a more useful form;
x%5E2-4x=0
highlight%28x%28x-4%29=0%29

EITHER x =0 OR x-4=0.
EITHER highlight%28x=0%29 OR highlight%28x=4%29.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(3x+4)=2+ sqrt(x)

square
%28sqrt%283x%2B4%29%29%5E2=%282%2B+sqrt%28x%29%29%5E2

3x%2B4+=+%282%29%5E2%2B%282%29%282%29%28sqrt%28x%29%29%2B%28sqrt%28x%29%29%5E2

3x%2B4=+4%2B4sqrt%28x%29%2Bx

rearrange
2x=+4sqrt%28x%29

square
4x%5E2=+16x


/4x
x=4