sqrt(3x+4)-sqrt(2x-4)=2

Question

Need help completing the square.

Answer 1

√(3x+4)-√(2x-4)=2, squaring:

3x+4-2√[(3x+4)(2x-4)]+2x-4=4,

5x-2√[(3x+4)(2x-4)]=4,

5x-4=2√[(3x+4)(2x-4)], squaring again:

25x²-40x+16=4(6x²-4x-16)=24x²-16x-64,

x²-24x+80=0=(x-4)(x-20).

So x appears to be 4 or 20. We need to substitute these into the original equation:

x=4: √16-√4=4-2=2, so x=4 is a solution.

x=20: √64-√36=8-6=2, so x=20 is also a solution.