Completing the square

Completing the square is a way to solve a quadratic equation if the equation will not factorise.

It is often convenient to write an algebraic expression as a square plus another term. The other term is found by dividing the coefficient of \(x\) by \(2\), and squaring it.

Any quadratic equation can be rearranged so that it can be solved in this way.

When completing the square, we end up with the form:

\[y=a(x\pm b)^2+c\]