Chapter SH, Problem 9.4.11EP

To determine

The value of c that makes each trinomial a perfect square.

Answer to Problem 9.4.11EP

The value of c is $49$ .

Explanation of Solution

Given:

The given equation is:

  $p^2-14p+c$

Calculation:

The solution of the given equation will be:

  $\begin{array}{l}\text{Step 1: Calculate }\frac{1}{2}\text{ of 14 }\frac{14}{2}=7\\ \text{Step 2: Square the result of Step 1 }{\left(7\right)}^2=49\\ \text{Step 3: Add the result of Step 2 to }{p}^2-14p{p}^2-14p+49\end{array}$

The value of c is 49.

Also, $p^2-14p+49={\left(p-7\right)}^2$