Question 74699
{{{x^4=16}}}  subtract 16 from both sides
{{{x^4-16=0}}}  Note that this can be factored. (We'll break the quartic equation into two quadratic equations and we know how to solve those).
{{{(x^2-4)(x^2+4)=0}}} so we have

{{{(x^2-4)=0}}} note that this can be factored
{{{(x+2)(x-2)=0}}}
{{{x=+2}}} --------------------------------------Ans#1
and 
{{{x=-2}}}------------------------------------------Ans#2

{{{(x^2+4)=0}}}  Actually this can be factored also

{{{(x+2i)(x-2i)=0}}}
{{{x=+2i}}}-----------------------------------------Ans#3
and
{{{x=-2i}}}----------------------------------------Ans#4

Lets look at solving the two quadratics in another way:

{{{x^2-4=0}}} add 4 to both sides
{{{x^2=4}}}  take sqrt of both sides

{{{sqrt(x^2)=sqrt(4)}}} or
{{{x=+2}}}
{{{x=-2}}}
and

{{{x^2+4=0}}} subtract 4 from both sides
{{{x^2=-4}}} take the sqrt of both sides

{{{sqrt(x^2)=sqrt(-4)}}} or
{{{x=+2i}}}
{{{x=-2i}}}


Hope this helps---ptaylor