/*! 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 40 Determine the constant that shou... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 40

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+5 x $$

Short Answer

Expert verified
The constant that should be added to the binomial is 6.25. The binomial becomes a perfect square trinomial \(x^{2}+5x+6.25\). The trinomial is factored as \((x + 2.5)^{2}\)

Step by step solution

01

Identify the a and b values in the binomial

The given binomial has the form \(x^{2}+5 x\). This is similar to the trinomial which is of form \(x^{2}+2ab+b^{2}\). Compare the binomial with the trinomial form, we can see that \(a=x\) and \(2ab=5 x\). So, we can solve for \(b\), \(b=(5 x)/(2*x)=2.5\).
02

Find the missing term for the perfect square trinomial

Now that we have a and b, we can now find the missing term that makes the binomial a perfect square trinomial. The missing term is \(b^{2}\), that is, \((2.5)^{2}=6.25\).
03

Write and factor the perfect square trinomial

The missing term \(6.25\) is added to the original binomial to make the perfect square trinomial, and we have \(x^{2}+5x+6.25\). This trinomial can be factored into \((x + 2.5)^{2}\).

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

Find all values of \(x\) satisfying the given conditions. $$ y_{1}=\frac{2 x}{x+2}, y_{2}=\frac{3}{x+4}, \text { and } y_{1}+y_{2}=1 $$

When 4 times a number is subtracted from 5, the absolute value of the difference is at most 13. Use interval notation to express the set of all numbers that satisfy this condition.

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. $$ (-\infty, 3) \cup(-\infty,-2)=(-\infty,-2) $$

A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 180 square yards. Find the length and the width.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

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.