help?

2/5x^6+2=27.6

Solve for x:
(2x^6)/5+2 = 27.6

27.6 = 138/5:
(2 x^6)/5+2 = 138/5

Subtract 2 from both sides:
(2 x^6)/5 = 128/5

Multiply both sides by 5/2:
x^6 = 64

Taking 6^th roots gives 2 times the 6^th roots of unity:
Answer: | 
| x = -2 or x = 2 or x = -2 (-1)^(1/3) or x = 2 (-1)^(1/3) or x = -2 (-1)^(2/3) or x = 2 (-1)^(2/3)

Nice answer, Guest....let me expand upon this, starting here:

x^6 = 64

x^6  - 64  =   0

(x^3  - 8) (x^3 + 8)  = 0

(x - 2) ( x^2 + 2x + 4) ( x + 2) ( x^2 - 2x + 4)  = 0

We  get the two real solutions of x = 2   and x = -2 by setting the first and third factors to  0 and solving

Then

x^2 + 2x + 4  = 0

x^2 + 2x + 1  = -4 + 1

(x + 1)^2  = -3

x + 1  = ( +/-)sqrt(3) i

x = (+/-) sqrt (3) i   - 1     produces two non-real solutions

And

x^2 - 2x + 4  = 0

x^2 - 2x + 1  = - 4 + 1

(x - 1)^2 = -3

x - 1  = (+/-)sqrt(3) i

x = (+/-)sqrt(3) i  + 1     produces the other two non-real solutions