Question #1ad28

1 Answer
Dec 13, 2017

#(x-2)/4 = (x+2)/(2x)# is the same as

#2x^2 - 4x = 4x +8 #

Explanation:

Bringing all terms to one side we get,

#2x^2 -4x -4x -8 = 0#
or
#2x^2 - 8x - 8 = 0#
Now see if there is any way to reduce the equation further.
Here we can factorize the entire equation by 2. We get,
#x^2 -4x -4 = 0#

#=> x^2-4x = 4 #

Completing the square:

We must plus the second term devided by 2 squared:

#=> x^2 - 4x + ((-4)/(-2))^2 = 4 + ( (-4)/(-2) ) ^2 #

#=> x^2 -4x +4 = 8#

#=> (x-2)^2 = 8 #

Square rooting both sides:

#=> x-2 = pm sqrt8 #

#=> x = 2 pm sqrt8 #

Simplify #sqrt 8 #

#sqrt 8 = 2sqrt2 #

#=> x = 2 pm 2sqrt2 #

#=> x = 2(1 pm sqrt 2 )#