Chapter 9.4, Problem 14E

To determine

To complete the square for expression.Then factor the trinomial.

  $x^2+22x$

Answer to Problem 14E

  $x^2+22x+121$

  $x^2+22x+121={(x+11)}^2$

Explanation of Solution

Given information:

Expression

  $x^2+22x$

Calculation:

Expression

  $x^2+22x$

Using the complete square algorithm

Step 1: Find $\frac{1}{2}$ of $22$

  $=\frac{1}{2}\times 22$

On solving

  $=11$

Step 2: Square the result in step 1

  ${(11)}^2=121$

Step 3: Add the result of step 2 to $x^2+22x$

Thus $c=121$

Notice that $x^2+22x+121$

Write the expression as product with the factor x and 11

  $x^2+2\times x\times 11+121$

On solving

  $x^2+2\times x\times 11+{11}^2$

Using $a^2+2ab+b^2={(a+b)}^2$

Then

  $x^2+22x+121={(x+11)}^2$