How would I solve 16x^4-41x^2+25=0 ???

First of all to make our equation simpler, we'll equal to a variable like 'a'.

So,



Now let's plug 's value (a) into the equation.



Now we turned our equation into a quadratic equation.

(The variable 'a' will have a solution set of two solutions, but 'x' , which is the variable of our first equation will have a solution set of four solutions since it is a quartic equation (fourth-degree equation) )

Let's solve for a.

The formula used to solve quadratic equations ;



The formula is used in an equation formed like this :



In our equation,

t=16 , b=-41 and c=25

Let's plug the values in the formula to solve.



So the solution set :



We found a's value.

Remember,



So after we found a's solution set, that means.



and



We'll also solve this equations to find x's solution set :)





So the values x has are :

, , and

Solution set :



I hope this was clear enough. If not please ask :)