/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 39 Determine the constant that shou... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 39

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+3 x $$

Short Answer

Expert verified
The constant needed to make the binomial a perfect square trinomial is 2.25. The trinomial is \(x^{2}+3 x+2.25\), which factors to \((x+1.5)^{2}\).

Step by step solution

01

Identify the coefficient of the x term

In the given binomial \(x^{2}+3 x\), the coefficient of the x term is 3.
02

Calculate the square of half of the coefficient of x term

Dividing the coefficient of x, which is 3, by 2 gives 1.5. Then, the square of 1.5 is calculated to be 2.25.
03

Add the obtained constant to the binomial to form a perfect square trinomial

Adding 2.25 to the given binomial \(x^{2}+3 x\) forms the perfect square trinomial \(x^{2}+3 x+2.25\). This is now a perfect square trinomial.
04

Factorize the formed perfect square trinomial

Using the property that the perfect square trinomial \(a^{2}+2ab+b^{2}\) can be factorized into \((a+b)^{2}\), the trinomial \(x^{2}+3 x+2.25\) can be factorized into \((x+1.5)^{2}\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises 59鈥�94, solve each absolute value inequality. $$ 1<\left|x-\frac{11}{3}\right|+\frac{7}{3} $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ (-\infty,-1] \cap[-4, \infty)=[-4,-1] $$

What is a quadratic equation?

Use the Pythagorean Theorem and the square root property to solve. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth. A baseball diamond is actually a square with 90 -foot sides. What is the distance from home plate to second base?

The length of a rectangular sign is 3 feet longer than the width. If the sign's area is 54 square feet, find its length and width.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.