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,} \\ (400)/(4)=(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_{}`