what are all the solutions for X^6+64?

x = 2

solution:

x^6 = -64
x = -square root of 64
x=2

Basics. Basics are lacking. You cannot solve an expression. Study algebra more seriously. Find out the difference between expression and equation, see which them can be "solved"
Find out more about squares of real numbers. Can they be negative?
Find out that sixth power is in fact a square of something.
You have to do a lot of algebra before you attempt any problems.

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

x^6 + 64
= (x^2)^3 + 64
= (x^2)^3 + 4^3
= (x^2 + 4)(x^4 - 4x^2 + 16)

That's an expression, not an equation. There are no solutions because there is nothing to "solve" here.

can't be solved unless you have = or inequality. Do you want to solve
x^6 = 64 ?

if so, the solutions are x = 2 or x = - 2.

good luck to you !


****After reading your second post, the only way to factor it is
(x^3 + 8i) (x^3 - 8i), where i is imaginary. Hope it helps !

okay first i need to know if the ^ is meant to be there and then i can answer