/*! 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 156 Explain how to solve \(x^{2}+6 x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 156

Explain how to solve \(x^{2}+6 x+8=0\) using factoring and the zero-product principle.

Short Answer

Expert verified
The solutions for the equation \(x^{2}+6 x+8=0\) are \(x = -2\) and \(x = -4\).

Step by step solution

01

Factorize the quadratic expression

Start by looking for two numbers that multiply to give +8 (the constant term) and sum to give +6 (the coefficient of \textit{x}). The numbers that satisfy these conditions are +2 and +4. So, the factorized form of the expression becomes \(x^{2}+6 x+8 = (x+2)(x+4)\).
02

Apply the Zero-Product Principle

according to the zero-product principle, if the equation \(ab = 0\), then \(a = 0\) or \(b = 0\). Apply this principle to find the values of \textit{x}, which produces the equations \(x + 2 = 0\) and \(x + 4 = 0\).
03

Solve for x

Solving the two equations from step 2 yields the solutions \(x = -2\) and \(x = -4\). These are the roots of the quadratic equation.

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

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(6(x-1)-(4-x) \geq 7 x-8\)

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(\frac{4 x-3}{6}+2 \geq \frac{2 x-1}{12}\)

Solve absolute value inequality. \(|x|<3\)

Solve absolute value inequality. \(5>|4-x|\)

Describe the solution set of \(|x|>-4\).
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.