Can you please show work? Thanks! *Note the x's are not part of the radicand Solve for x

sqrt2 x(3sqrt2 x-6)=0

1 Answer
Mar 1, 2018

x=0, x=sqrt(2)

Explanation:

Apply the Distributive Property, a(b+-c)=ab+-ac

sqrt(2)x(3sqrt(2)x-6)=sqrt(2)x*3sqrt(2)x-sqrt(2)x*6

3sqrt(2)^2x^2-6sqrt(2)x=0

3(2)x^2-6sqrt(2)x=0 (Because sqrt(a)^2=a)

6x^2-6sqrt(2)x=0

Both of our terms include an instance of 6x, so we can factor out 6x:

6x(x-sqrt(2))=0

We now have two equations two solve for x:

6x=0 and x-sqrt(2)=0

6x=0

(cancel6x)/cancel6=0/6

x=0

So, x=0 is one of our answers.

x-sqrt(2)=0

xcancel(-sqrt(2)+sqrt(2))=0+sqrt(2)

x=sqrt(2)

So, x=sqrt(2) is our other answer.