Question

Question #1ad28

Answer 1

`(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 )`