Math Quadratic equations Mixed quadratic equations

Mixed quadratic equations

A mixed quadratic equation is an equation in the form:


Mixed quadratic equations can be solved with the help of completing the square.



  1. If a coefficient is before the $x^2$, it must be excluded beforehand, for example:

  2. Completing the square on both sides of the equation

  3. Apply binomial formula backwards $(x+\color{red}{\frac{p}{2}})^2=-q+\color{red}{(\frac{p}{2})^2}$

  4. Calculate square root and put $x$ on one side


  1. Determine $p$:


  2. Completing the square $+(\frac{p}{2})^2$:


  3. Apply binomial formula backwards and calculate square root


  4. Put $x$ alone on one side of the equation

    There are two solutions (one positive and one negative square root)


  5. $x_1=-1$ and $x_2=-19$