Question

How would I solve this:
sqrt(-2 x)-(sqrt(5-x)) = -3/(sqrt(5-x))

Answer 1

i would start by multiplying both sides by \(\sqrt{5-x}\) to get
\[\sqrt{2x(5-x)}-(5-x)=-3\]

Answer 2

ok

Answer 3

I've done that

Answer 4

now rewrite as
\[\sqrt{-2x(5-x)}=-3+5-x=2-x\]

Answer 5

square both sides and get \[-2x(5-x)=(2-x)^2\]

Answer 6

then \[2x^2-10x=x^2-4x+4\] and you have a quadratic equation to solve

Answer 7

okay!

Answer 8

\[x^2-6x-4=0\]

Answer 9

x=6.60555127546399 x=−0.6055512754639891

Answer 10

then easiest to complete the square
\[x^2-6x=4\]
\[(x-3)^2=4+9=13\]
\[x-3=\pm\sqrt{13}\]
\[x=3\pm\sqrt{13}\]

Answer 11

you can check that this is right here https://www.wolframalpha.com/input/?i=sqrt%28-2+x%29-%28sqrt%285-x%29%29+%3D+-3%2F%28sqrt%285-x%29%29

Answer 12

cool, thanks so much!