How to solve for x in this equation?

Question

f(x) = x^4-2(x^2)-1

Answer 1

x^4-2(x^2)-1=0

Let  x^2=t

t^2-2t-1=0

Using quadratic formula

t=(-b+sqrt(b^2-4ac))/2a or (-b-sqrt(b^2-4ac))/2a

t=(2+sqrt(4+4))/2

  =(1+sqrt(2))

x^2=(1+sqrt(2))

x=sqrt(1+sqrt(2))

Comments

t = (- b ± √(b^2 - 4ac))/2a.

a = 1, b = - 2, and c = - 1.

t = (2 ± √((- 2)^2 - 4*1*(- 1)))/2*1

t = (2 ± √(4 + 4))/2

t = (2 ± √8)/2

t = (2 ± 2√2)/2

t = 1 ± √2

put, t = x^2.

x^2 = 1 ± √2

⇒ x = ± √(1 ± √2).