Quadratic equation

Question

Hi, I need help solving this : 

 

[(1)/(2x)+(5)]^2 = 12 

Answer 1

first we apply square root to both side to get

1/(2x) +5=±2√3

so we have 1/(2x) + 5=2√3 or 1/(2x)+5=-2√3

                 1/(2x)=2√3-5    or 1/(2x)=-2√3-5

                  2x=1/(2√3-5)   or  2x=1/(-2√3-5)

                   x=1/(4√3-10) or x=1/(-4√3-10)

 

this is assuming that (2x+5) is not in one denominator 

Answer 2

(1/(2x)+5)² = 12

 

we use the formula (a+b)² = a² + 2ab +b²

 

therefore: (1/(2x))² + 2(1/(2x))(5)+ 5² =12

1/(4x²) + 10/(2x) + 25 = 12

1/(4x²) + 5/x = 12-25 

Multiply both sides by 4x²:  1 + 4x²(5/x) = -13(4x²)

Simplify: 1 + 20x = -52x²

Rearranging: 52x² + 20x + 1 = 0 

 

Then using the quadratic formula solve for x, where a = 52, b = 20 and c= 1 

 

You should end up with (-20 +/- sqrt(192))/104