Question #1ad28

1 Answer
Dec 13, 2017

(x-2)/4 = (x+2)/(2x)x24=x+22x is the same as

2x^2 - 4x = 4x +8 2x24x=4x+8

Explanation:

Bringing all terms to one side we get,

2x^2 -4x -4x -8 = 02x24x4x8=0
or
2x^2 - 8x - 8 = 02x28x8=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 = 0x24x4=0

=> x^2-4x = 4 x24x=4

Completing the square:

We must plus the second term devided by 2 squared:

=> x^2 - 4x + ((-4)/(-2))^2 = 4 + ( (-4)/(-2) ) ^2 x24x+(42)2=4+(42)2

=> x^2 -4x +4 = 8x24x+4=8

=> (x-2)^2 = 8 (x2)2=8

Square rooting both sides:

=> x-2 = pm sqrt8 x2=±8

=> x = 2 pm sqrt8 x=2±8

Simplify sqrt 8 8

sqrt 8 = 2sqrt2 8=22

=> x = 2 pm 2sqrt2 x=2±22

=> x = 2(1 pm sqrt 2 )x=2(1±2)