Completing the square

Given any monic quadratic $x^2+bx+c=$.

it is possible to form a square that has the same first two terms: $x^2+bx+\frac{b^2}{4}={\left(x+\frac{b}{2}\right)}^2$his square differs from the original quadratic only in the value of the constant term. Therefore, we can write $x^2+bx+c={\left(x+\frac{b}{2}\right)}^2+\left(c-\frac{b^2}{4}\right)$

• A square number (or perfect square) is an integer that is the square of an integer