Chapter 7.1, Problem 19OE

To determine

To Find:

What must be added to make the expression a trinomial square:

  $r^2-\frac{1}{2}r+?$

Answer to Problem 19OE

  $\frac{1}{16}$

Explanation of Solution

Given:

The expression is :

  $r^2-\frac{1}{2}r+?$

Calculation:

Given:

  $r^2-\frac{1}{2}r+?$

First , make the coefficient of $r^2$ 1.

Since here , it already is 1.

Check for the coefficient of r .

It is $\frac{1}{2}$ .

So, the term that has to be added to make it a trinomial and a perfect square is :

square of the half of the coefficient of r

  $={\left(\frac{1}{2}\cdot \frac{1}{2}\right)}^2=\frac{1}{16}$

So, $\frac{1}{16}$ should be added.

Check:

  $r^2-\frac{1}{2}r+\frac{1}{16}={\left(r-\frac{1}{4}\right)}^2$