Math Quadratic equations Pure quadratic equations

Pure quadratic equations

A purely quadratic equation is an equation in the form:


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



  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:

  2. To get $x$, the square root must be calculated:

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


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


  1. $900$ on the other side

  2. Calculate square root

    (both from $x^2$ and from $900$)

  3. Two results

    because: $30^2=(-30)^2=900$