x^4 + 50 = 0

Question

x to the 4th power plus fifty equals zero; solve for x. Please let me know the steps to do to arrive at the solution.

Answer 1

x^4+50=0 ---------- 1
consider x^2=p
p^2+50=0
p^2=-50
multiply (-) on both sides
-p^2 = (25 *2 )
-p^2= (5^2 * 2)
taking square root on both sides
- p = 5 sqrt 2
as we know that p= x^2 
- x^2 = 5 sqrt 2
- x =sqrt 5.fourth root of 2
i.e x = - (sqrt 5 * fourth root of 2)

for checking substitute with equation 1

(- (sqrt 5 * fourth root of 2))^4 + 50 =0
-50 + 50 =0