Chapter 9: Q.413. (page 982)

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$a^{2} - 3 a$

Short Answer

Expert verified

The solution is ${(a - \frac{3}{2})}^{2}$ .

Step by step solution

Step 1. Given information.

The given binomial expression is $a^{2} - 3 a$ .

Step 2. Identify b, the coefficient of a.

The given binomial expression is $a^{2} - 3 a$ .

Comparing the given expression with $a^{2} + b a$ , we have $b = - 3$ .

Thus, the coefficient of $a$ is $- 3$ .

Step 3. Find the number to complete the square.

$\begin{array}{rcl} {(\frac{1}{2} b)}^{2} & = & {(\frac{1}{2} (- 3))}^{2} \\ = & \frac{9}{4} \end{array}$

Thus, the number to complete the square is $\frac{9}{4}$ .

Step 4. Now, complete the square.

Add $\frac{9}{4}$ to the given binomial expression.

$\begin{array}{rcl} a^{2} - 3 a + \frac{9}{4} & = & a^{2} - 2 \cdot a \cdot \frac{3}{2} + {(\frac{3}{2})}^{2} \\ = & {(a - \frac{3}{2})}^{2} \end{array}$

Step 5. Simplified answer.

Hence, the required complete square trinomial is ${(a - \frac{3}{2})}^{2}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$a^{2} - 3 a$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Identify b, the coefficient of a.

Step 3. Find the number to complete the square.

Step 4. Now, complete the square.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Probability and Statistics

Logic and Functions

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.a2-3a

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Identify b, the coefficient of a.

Step 3. Find the number to complete the square.

Step 4. Now, complete the square.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Probability and Statistics

Logic and Functions

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
$a^{2} - 3 a$