Question

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

Answer 1

The general formula for quadractic expression is given as,

$ax^2+bx+c$

The expression given is,

$w^2-20w$

Comparing the two expressions.

where,

$\begin{gathered} a=1 \\ b=-20 \\ c=\text{?} \end{gathered}$

To solve for c, which is the value that will be added to the expression to make it a perfect trinomial. We will apply discriminant formula.

$b^2-4ac=0$$\begin{gathered} (-20)^2-4(1)c=0 \\ 400-4c=0 \\ 400=4c \\ \text{divide both sides by 4,} \\ \frac{400}{4}=\frac{4c}{4} \\ 100=c \\ \Rightarrow c=100 \end{gathered}$

The trinomial expression will now be,

$\begin{gathered} w^2-20w+c \\ \text{where c=100} \\ w^2-20w+100 \end{gathered}$

Let us now factorize the expression inorder to write it as a binomial squared,

$\begin{gathered} w^2-20w+100 \\ w^2-10w-10w+100 \\ w(w-10)-10(w-10) \\ (w-10)(w-10)=(w-10)^2_{} \end{gathered}$

Hence, the result as a binomial squared is,

$(w-10)^2_{}$