/*! 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 41 Explain how to complete the squa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 41

Explain how to complete the square for a binomial. Use \(x^{2}+6 x\) to illustrate your explanation.

Short Answer

Expert verified
The completed square form of the given expression \(x^{2} + 6x\) is \((x+3)^{2}\).

Step by step solution

01

Identify the quadratic expression.

For the given quadratic expression \(x^{2} + 6x\), the coefficients of \(x^{2}\) and \(x\) are 1 and 6 respectively.
02

Determine the term needed to complete the square.

To complete the square, the formula \((b/2)^{2}\) is employed, where 'b' is the coefficient of 'x'. In this case, \(b=6\). Substituting the value of 'b' into the formula gives \((6/2)^{2}=(3)^{2}=9\).
03

Form a perfect square trinomial

Add the determined value to the given quadratic expression to form a perfect square trinomial. Here, we add 9 to \(x^{2} + 6x\) to get \(x^{2} + 6x + 9\).
04

Factor the perfect square trinomial

Factor the perfect square trinomial, \(x^{2} + 6x + 9\), which becomes \((x+3)^{2}\). That value is the completed square form of the original expression.

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

If a relation is represented by a set of ordered pairs, explain how to determine whether the relation is a function.

Solve each equation or system of equations. $$7(x-2)=10-2(x+3)$$

The distance, \(d,\) in feet, that an object falls in \(t\) seconds is modeled by the formula \(d=16 t^{2} .\) Use this formula to solve Exercises \(75-76\) If you drop a rock from a cliff 400 feet above the water how long will it take for the rock to hit the water?

Divide: \(\frac{x^{3}+7 x^{2}-2 x+3}{x-2}\)

Explain how to solve \((x-1)^{2}=16\) using the square root property.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.