# How do you solve quadratic equations to the fourth power?

Jul 21, 2018

The most common way to solve a quadratic equation to the fourth power would be using ${x}^{2}$ instead of $x$ when factoring, an example is shown below.

#### Explanation:

Depending on the specific problem, there are different ways that you may be able to solve the quadratic equation.

Sometimes, you are able to factor each term by a numerical value, an example where this can be used is

$4 {x}^{4} + 8 {x}^{3} + 2 {x}^{2} + 12 x + 24 = 0$

In this situation, you would be able to divide each term by $2$

Another situation would be ${x}^{4} + 4 {x}^{2} + 4$

In this situation, you would factor like a quadratic that goes to the second power with the exception of the first term of each set of parentheses will be ${x}^{2}$ instead of $x$, giving you
$\left({x}^{2} + 2\right) \left({x}^{2} + 2\right)$

This would be the most common way of solving quadratic equations to the fourth power, but depends on the problem that is given.