Question

PLEASE SOLVE AND SHOW STEPS!!!!! (x-4)-5(x-4)^.5=6

Answer 1

\[(x-4)-5(x-4)^{.5}=6\]
Isolate
\[(x-4)^{.5}\] on the left. Square both sides. You should get

...

my answer's ugly, though, are you sure you've written it out correctly. Or have I made a mistake?

Answer 2

gimmick is to write
\[(x-4)-5\sqrt{x-4}-6=0\] and then since
\[(x-4)=\sqrt{x-4}^2\] you have a quadratic equation in \[\sqrt{x-4}\]

Answer 3

i.e. put
\[z=\sqrt{x-4}\]and then solve \[z^2-5x-6=0\]
\[(z-6)(z+1)=0\]
\[z=6\] so
\[\sqrt{x-4}=6\]
\[x-4=36\]
\[x=40\]

Answer 4

ohhhhh... duh

Answer 5

notice you can ignore
\[\sqrt{x-4}=-1\] because it is not possible.
another solution would be to write
\[-5\sqrt{x-4}=6-x+4=10-x\] and then square both sides to get
\[25(x-4)=100-20x+x^2\]
\[25x-100=100-20x+x^2\]
\[x^2-45x+200=0\]
\[(x-40)(x-5)=0\]
\[x=40\] or
\[x=5\] but the check will show that 5 does not work