Pure quadratic equations
A purely quadratic equation is an equation in the form:
$x^2q=0$
A purely quadratic equation can usually be solved very quickly by switching and root extraction.
i
Method

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:
$x^2q=0\quad+q$ 
To get $x$, the square root must be calculated:
$x^2=q\quad\pm\sqrt{}$ 
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.
Example

$900$ on the other side
$x^2900=0$\quad+900$ 
Calculate square root
(both from $x^2$ and from $900$)
$x^2=900\quad\pm\sqrt{}$ 
Two results
because: $30^2=(30)^2=900$
$x_1=30$
$x_2=30$