/*! 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 74 Solve each equation by the metho... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 74

Solve each equation by the method of your choice. \(\frac{x^{2}}{3}-\frac{x}{2}-\frac{3}{2}=0\)

Short Answer

Expert verified
The solutions to the equation are \(x=1\) and \(x=-1.5\).

Step by step solution

01

Identify the coefficients

The first part of this problem is to identify coefficients a, b, c from the equation \(\frac{x^{2}}{3}-\frac{x}{2}-\frac{3}{2}=0\). In this case, \(a=\frac{1}{3}\), \(b=-\frac{1}{2}\), and \(c=-\frac{3}{2}\).
02

Substitute coefficients into the quadratic formula

The next step is to substitute these coefficients into the quadratic formula. This gives: \[x=\frac{-(-\frac{1}{2}) \pm \sqrt{(-\frac{1}{2})^2-4*\frac{1}{3}*-(\frac{3}{2})}}{2*\frac{1}{3}}\]. Simplifying this equation will give the solutions for x.
03

Simplify the equations to get solutions

Solving these two equations give the values of x as 1 and -1.5. Thus, the solutions to the equation are \(x=1, x=-1.5\).

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 98-99, find all positive integers b so that the trinomial can be factored. \(x^{2}+b x+15\)

Solve the equations using the quadratic formula. \(x^{2}+4 x+1=0\)

Solve each equation by the method of your choice. \(2 x^{2}-9 x-3=9-9 x\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-x-90\)

Solve the equations using the quadratic formula. \(x^{2}-3 x=10\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete 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.