Completing the Square

We want to complete the square for the given expression. To do so, we will first identify $b.$ In a quadratic trinomial, $b$ is the linear coefficient, which is the number that is multiplied by the $x$-variable. $$\begin{array}{c}{x}^2+24x+c\end{array}$$ Now, we will calculate ${\left(\frac{b}{2}\right)}^2.$ Since we have that $b=24,$ we can calculate the value of ${\left(\frac{b}{2}\right)}^2$ by substituting $24$ for $b.$ When the value of $c$ is $144$ our expression is a perfect square trinomial. $$\begin{array}{c}{x}^2+24x+144\end{array}$$ Now we can write this expression as the square of a binomial.