find all exact real solutions of the equation.

Question

x^4-2x^2-24=0

Answer 1

Use the substitution
y=x²
y²-2y-24=0
factorize
(y-6)(y+4)=0
y=6, y=-4
x²=6 ... (1)
x²=-4 ... (2)
(1) gives x=±√6 (real solutions)
(2) gives x=±2i (complex solutions, discarded)

Answer 2

X²+y²+2y-24=0