Question

how can i solve for x in sqrt of 2x-4 minus sqrt of x-5 = 3

Answer 1

maybe
\[\sqrt{2x-4}-\sqrt{x-5}=2\]

Answer 2

yeah thats right, but its = 3 not 2

Answer 3

start with
\[\sqrt{2x-4}=\sqrt{x-5}+3\] and square both sides

Answer 4

this is going to be a drag because you are going to have to square twice, and also check your answer. first time you get
\[2x-4=x-5+9+6\sqrt{x-5}\]

Answer 5

this gives
\[x-8=6\sqrt{x-5}\] and then square again to get
\[(x-8)^2=36(x-5)\]
\[x^2-16x+64=36x-180\]
\[x^2-52x+244=0\]

Answer 6

then i guess you can solve using the quadratic formula, but the numbers are so annoyingly large it might be easier to complete the square. your choice

Answer 7

thanks