SOLUTION: Please help.... I watched a video on Khan Academy to complete this but I just do not understand it... Any help would be appreciated. find all real solutions for x6 + 56x^3 – 512

Algebra ->  Radicals -> SOLUTION: Please help.... I watched a video on Khan Academy to complete this but I just do not understand it... Any help would be appreciated. find all real solutions for x6 + 56x^3 – 512      Log On


   

Question 737222: Please help.... I watched a video on Khan Academy to complete this but I just do not understand it... Any help would be appreciated.
find all real solutions for x6 + 56x^3 – 512 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint:

Let z = x^3. So squaring both sides gives us z^2 = (x^3)^2 = x^6. This means

z = x^3

z^2 = x^6

-------------------------------------------------------

So

x^6 + 56x^3 – 512 = 0

turns into

z^2 + 56z – 512 = 0

Your next task is to solve for z. I'll let you do this. You would use the quadratic formula to solve for z.

Once you have 2 solutions for z, you then use each solution of z to find the solutions for x.