How do you solve for x in the simplest radical form for (x^2+2x+4)/x =(2x)/1?

1 Answer
Apr 14, 2015

If a/b=c/d->a*d=b*c this is called cross-product.

Applying this, we have:

(x^2+2x+4)*1=x*2x->

x^2+2x+4=2x^2->

Subtract 2x on both sides and multiply by -1

x^2-2x-4=0

There are several ways to solve this. I will rewrite for the square:

(x^2-2x+1)-5=0->
(x-1)^2-5=0->
(x-1)^2=5->
x-1=+sqrt5or-sqrt5->

Solution:

x=1+sqrt5orx=1-sqrt5