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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.414. (page 982)

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$b^{2} + 13 b$

Short Answer

Expert verified

The solution is ${(b + \frac{13}{2})}^{2}$ .

Step by step solution

01

Step 1. Given information.

The given binomial expression is $b^{2} + 13 b$ .

02

Step 2. Identify the coefficient of b.

Comparing the given binomial expression with $b^{2} + a b$ .

We have $a = 13$ .

So, the coefficient of $b$ is $13$ .

03

Step 3. Find the number to complete the square.

$\begin{array}{rcl} {(\frac{1}{2} a)}^{2} & = & {(\frac{1}{2} 路 13)}^{2} \\ = & \frac{169}{4} \end{array}$

04

Step 4. Now complete the square.

Add $\frac{169}{4}$ to the given binomial expression.

$\begin{array}{rcl} b^{2} + 13 b + \frac{169}{4} & = & b^{2} + 2 路 b 路 \frac{13}{2} + {(\frac{13}{2})}^{2} \\ = & {(b + \frac{13}{2})}^{2} \end{array}$

05

Step 5. Simplified answer.

Hence, the required complete square trinomial is $\begin{array}{rcl} {(b + \frac{13}{2})}^{2} \end{array}$ .

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