/*! 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 129 Solve each equation by the metho... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 129

Solve each equation by the method of your choice. $$\sqrt{2} x^{2}+3 x-2 \sqrt{2}=0$$

Short Answer

Expert verified
The solutions to the equation \(\sqrt{2} x^{2}+3 x-2 \sqrt{2}=0\) are \(x = \frac{-3 + \sqrt{17}}{2}\) and \(x = \frac{-3 - \sqrt{17}}{2}\)

Step by step solution

01

Identify the coefficients

The equation given is \(\sqrt{2} x^{2}+3 x-2 \sqrt{2}=0\). Here, \(a = \sqrt{2}\), \(b = 3\), and \(c = -2\sqrt{2}\)
02

Apply the quadratic formula

We can solve this quadratic equation by using the quadratic formula: \(x = \frac{-b \pm \sqrt{{b^2} - 4ac}}{2a}\). Replacing \(a\), \(b\) and \(c\) with their respective values from the given equation-\(x = \frac{-3 \pm \sqrt{{3^2} - 4*(\sqrt{2})*(-2\sqrt{2})}}{2*\sqrt{2}}\)
03

Simplify the Expression

Upon simplification, the solution to the equation is \(x = \frac{-3 \pm \sqrt{9 + 8}}{2\sqrt{2}}\) = \(\frac{-3 \pm \sqrt{17}}{2\sqrt{2}}\). Now use rationalizing factor to get rid of square root value in denominator. Ultimately the solutions are \(x = \frac{-3 + \sqrt{17}}{2}\) or \(x = \frac{-3 - \sqrt{17}}{2}\).

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

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

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(-4(x+2)>3 x+20\)

Solve absolute value inequality. \(|3(x-1)+2| \leq 20\)

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and 88 . There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90 . a. What must you get on the final to earn an A in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than \(80,\) you will lose your \(\mathrm{B}\) in the course. Describe the grades on the final that will cause this to happen.

Describe ways in which solving a linear inequality is different than solving a linear equation.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

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.