/*! 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 75 Solve. $$ x^{2}=6+x $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 75

Solve. $$ x^{2}=6+x $$

Short Answer

Expert verified
x = 3 or x = -2

Step by step solution

01

Bring all terms to one side

First, bring all terms to one side of the equation to set it equal to zero. Subtract \(x\) and 6 from both sides of the equation: \( x^2 - x - 6 = 0 \).
02

Factor the quadratic equation

Next, factor the quadratic equation. Look for two numbers that multiply to \(-6\) (the constant term) and add to \(-1\) (the coefficient of \(x\)). These numbers are \(-3\) and 2. So, the equation factors to: \( (x - 3)(x + 2) = 0 \).
03

Solve for x

Set each factor equal to zero and solve for \(x\): \(x - 3 = 0\) gives \(x = 3\). \(x + 2 = 0\) gives \(x = -2\).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

factoring quadratics
When solving quadratic equations, factoring quadratics is a key step. A quadratic equation is typically in the form \( ax^2 + bx + c = 0 \). To factor, we need to find two numbers that both multiply to the constant term (\

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

Knitted fabric is described in terms of wales per inch (for the fabric width) and courses per inch (CPI) (for the fabric length). The CPI \(c\) is inversely proportional to the stitch length \(l .\) For a specific fabric with a stitch length of 0.166 in. the CPI is \(34.85 .\) What would the CPI be if the stitch length were increased to 0.175 in.?

Factor completely. $$ 8 x^{3}+125 \quad[5.6] $$

Find the domain of \(f\). \(f(x)=\sqrt{2 x+8}\)

Wind power \(P\) from a turbine varies directly as the square of the length of one of its blades \(r .\) If the blade length is doubled, is the wind power doubled as well? Why or why not?

Find an equation of variation in which: \(y\) varies jointly as \(x\) and \(z,\) and \(y=105\) when \(x=14\) and \(z=5\).
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

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.