Chapter 7.2, Problem 66STP

Yy13

To determine

To find: The value of $c$ that makes each trinomial a perfect square and then write the trinomial as a perfect square.

Answer to Problem 66STP

The value of $c$ is $\frac{121}{4}$ and trinomial can be written as a perfect square as ${\left(x-\frac{11}{2}\right)}^2$ .

Explanation of Solution

Given:

The trinomial is $x^2-11x+c$ .

Calculation:

Find the one half of 11 as $\frac{11}{2}$ .

Squaring the above result as follows.

  ${\left(\frac{11}{2}\right)}^2=\frac{121}{4}$

So, the value of $c$ is $\frac{121}{4}$ .

Substitute $\frac{121}{4}$ for $c$ in the given equation.

  $x^2-11x+\frac{121}{4}={\left(x-\frac{11}{2}\right)}^2$

Therefore, the value of $c$ is $\frac{121}{4}$ and trinomial can be written as a perfect square as ${\left(x-\frac{11}{2}\right)}^2$ .