A purely quadratic equation is an equation in the form:

$x^2-q=0$

A purely quadratic equation can usually be solved very quickly by switching and root extraction.

i

### Method

1. First, $q$ has to be put on the other side of the equation so that $x^2$ stands alone. For this, add $q$ on both sides of the equation:
$x^2-q=0\quad|+q$

2. To get $x$, the square root must be calculated:
$x^2=q\quad|\pm\sqrt{}$

3. Finally, we get two results. Once the positive and once the negative square root of $q$:
$x_{1}=+\sqrt{q}$ und $x_{2}=-\sqrt{q}$
!

### Remember

$x^2+q=0$ has no solution.