Completing The Square

A process to find the roots of a quadratic function, Given $a{x}^2+bx+c=0$

• Divide whole equation by $a$
• Get $(x+\frac{b}{2}{)}^2$
• Find the $d$ which is the $c$-offset
• $=\left(x+\frac{b}{2}\right)+d$ Often used for integrating reciprocal polynomial functions

Example

$x^2-6x+13$

• Choose $(x-3{)}^2=x^2-6x+9$
• $⟹x^2-6x+13=(x-3{)}^2+4=$