Solve for X. 16X-16= -1/x

Question

Solve for X. 16X-16= -1/x   Thank you!

Answer 1

16x - 16 = -1/x

 

16x^2 - 16x + 1 = 0

 

a = 16, b = -16, c = 1

 

x = (-b ± √(b^2 - 4ac))/(2a)

 

x = (-(-16) ± √((-16)^2 - 4(16)(1)))/(2(16))

 

x = (16 ± √((16)(16 - 4)))/(2(16))

 

x = (16 ± √((16)(4)(4 - 1)))/(2(16))

 

x = (16 ± 8√(3))/(2(16))

 

x = (2 ± √(3))/4

 

check:

 

16((2 ± √(3))/4) - 16 =? -1/((2 ± √(3))/4)

 

16(((2 ± √(3))/4) - 4/4) =? -4(-2 ± √(3))/((2 ± √(3))(-2 ± √(3)))

4( -2 ± √(3) ) =? -4(-2 ± √(3))/(-4 + 3)

 

4( -2 ± √(3) ) =? 4(-2 ± √(3)) √

 

Answer 2

16 X - 16 = - 1/X

                                                

 16X^2 - 16X + 1 = 0

 

   X =  16 ± √ (-8) ^2 - 16

          16         16

 

          1  ± √48

                  16

 

          1 ± 4√3

                 16

          1 ± √3

                 4