Math Quadratic equations Completing the square

Completing the square

Completing the square is used to transform a term so that one can apply the first or second binomial formula backwards.



  1. Square term with the form:
    Important: If a coefficient is before $x^2$, it must be excluded beforehand

  2. Completing the square

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


Completing the square is often used to get a quadratic function in the vertex shape or to solve a mixed quadratic equation.


Put the function $f(x)=2x^2-80x$ into the vertex shape

  1. Exclude coefficient before $x^2$

  2. Apply completing the square

  3. Apply 2nd binomial formula backwards and resolve parenthesis