What are the real and complex solutions of the polynomial equation? x^4-41x^2=-400 show your work

The real solutions are -5, -4, 4, 5. There are no complex solutions.

The equation ...

... x^4 -41x^2 +400 = 0

can be factored as ...

... (x^2 -16)(x^2 -25) = 0

... (x -4)(x +4)(x -5)(x +5) = 0

So, all roots are real and are ...

... x ∈ {-5, -4, 4, 5}

These are the values of x that make the factors zero.

gdp is the best phrase!

using pemdas, (order of operations) you'll see the answer is 24.