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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.411. (page 982)

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$x^{2} + 22 x$

Short Answer

Expert verified

The solution is ${(x + 11)}^{2}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $x^{2} + 22 x$ .

02

Step 2. Compare the given expression with x2+bx.

The given binomial expression is $x^{2} + 22 x$ .

On comparing with $x^{2} + b x$ , we have $b = 22$ .

So, the coefficient of $x$ is $22$ .

03

Step 3. Find the 12b2.

$\begin{array}{rcl} (\frac{1}{2} b^{2}) & = & {(\frac{1}{2} 路 22)}^{2} \\ = & {(11)}^{2} \\ = & 121 \end{array}$

Thus, the number to complete the square is $121$ .

04

Step 4. To complete the square, add 121in the given binomial expression.

$\begin{array}{rcl} x^{2} + 22 x + 121 & = & x^{2} + 2 路 x 路 11 + {(11)}^{2} \\ = & {(x + 11)}^{2} \end{array}$

05

Step 5. Simplified answer.

Hence, the required binomial square is $\begin{array}{rcl} {(x + 11)}^{2} \end{array}$ .

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