Solve issuing quadratic techniques

x^4 - 29x^2 + 100 = 0

Define y = x².

Then the given equation may be written as

y² - 29y + 100 = 0

Factorize to obtain

(y - 4) (y - 25) = 0

The solutions are

y = 4 or y = 25

Because y = x², obtain

x² = 4 = > x = 2 or x = - 2.

x² = 25 = > x = 5 or x = - 5

The solution for x is 2, - 2, 5, - 5.

A plot of the function (shown below) verifies that the answer is correct.

Answer: x = 2, - 2, 5, - 5