Math Quadratic equations Pure quadratic equations

Pure quadratic equations

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.

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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.

Example

  1. $900$ on the other side


    $x^2-900=0$\quad|+900$
  2. Calculate square root

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

    $x^2=900\quad|\pm\sqrt{}$
  3. Two results

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

    $x_1=30$
    $x_2=-30$