The given equation is :[tex]x^{4} -5x^{2}-14=0[/tex]
Let [tex]x^{2} =y[/tex]
The given equation reduces to :
[tex]y^{2}-5y-14=0.[/tex]
Factoring the equation we have:
(y-7)(y+2)=0
Solving the equations for y:
y-7=0 y+2=0
Or y=7. Or y=-2.
Substituting y value:
[tex]x^{2} =7[/tex] [tex]x^{2} =-2[/tex]
Or x=+2.64,-2.64. Square root of negative number is not real. x=[tex]\sqrt{-2} =+i\sqrt{2} ,-i\sqrt{2}[/tex]
X= -2.64,+2.64,[tex]i\sqrt{2} ,-i\sqrt{2}[/tex]
