Question

Solve 6x=the square root of (24 +12x).
Check for extraneous solutions.

Answer 1

6x=sqrt(24+12x)

(6x)^2 = 24+12x

36x^2 -12x -24 = 0


x= -2/3 or x= 1


if you substitute x=-2/3 on the main equation:

6x=sqrt(24+12x)
6*(-2/3)=sqrt(24+12(-2/3))
-4 = 4


if you substitute x=1 on the main equation:

6x=sqrt(24+12x)
6=sqrt(24+12)
6=6


so the only solution is x=1