+0

# solve for x

0
192
2

Hi there,

I'm having trouble solve for x in this equation.

I've checked the equation a few times, it's correct!

Oct 25, 2018

#1
+102320
+1

Here's my  best attempt :

0   =    w         ( L^2x^2     -   x^4      -  7L^4  )

____        ______        ___         _____

EI6L           2                 4             60

Multiply both sides by   EI6L / w     and the lead term "disappears"

0  =   L^2 x^2     -   x^4     -  7L^4

______         ____      _____

2                4            60

Multiply through by  - 60

15x^4  -  30L^2x^2  +  7L^4   =   0

15x^4  -  30L^2x^2     =  -  7L^4         factor  out 15

15 ( x^4 - 2L^2x^2)  = - 7L^4            divide both sides  by 15

x^4  - 2L^2x^2   =     - 7L^4 / 15

Take  1/2  of 2L^2  = L^2

Square this  = L^4

x^4 - 2L^2 x^2  + L^4  =   -7L^4 / 15   + L^4

Factor the left side   and simplify

( x^2  - L^2)^2  =   8L^4 / 15

Take both roots  and simplify

x^2  - L^2  =   ±√ [ (8L^4 / 15) ]

x^2 - L^2  =  ±2L^2√ [ 2/15 ]

x^2  =  L^2  ± 2L^2√ [ 2/15 ]

Take both roots again

x =  ±√ ( L^2 ± 2L^2√ [ 2/15 ]  )  =    ± L√ ( 1 ± 2√ [ 2/15 ]  )

Oct 25, 2018
edited by CPhill  Oct 25, 2018
edited by CPhill  Oct 25, 2018
edited by CPhill  Oct 25, 2018
edited by CPhill  Oct 25, 2018
#2
+1

how b****y painful.

thank you!

Oct 25, 2018