/*! 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 63 Solve each quadratic equation by... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 63

Solve each quadratic equation by the square root property. $$5 x^{2}+1=51$$

Short Answer

Expert verified
The solution to the equation is \(x = \sqrt{10}\) and \(x = -\sqrt{10}\)

Step by step solution

01

Simplify the equation

To simplify the equation and isolate the square term on one side of the equation, we subtract 1 from both sides of the given equation. We therefore obtain:\[5x^2 = 51 - 1 = 50\]
02

Isolate the square term

Now, to fully isolate the square term \(x^2\), we divide every term of the equation by 5 to obtain:\[x^2 = \frac{50}{5} = 10\]
03

Apply the square root property

Applying the square root property to our equation, we find the two potential values for \(x\). Remember, if \(x^2 = a\), then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\). Thus we get:\[x = \sqrt{10}\] or \[x = -\sqrt{10}\]

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

Explain how to divide rational expressions.

What is a rational expression?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cost \(\$ 175 .\) The mechanic charges \(\$ 34\) per hour. If you receive an estimate for at least \(\$ 226\) and at most \(\$ 294\) for fixing the car. what is the time interval that the mechanic will be working on the job?

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.

Explain why \(|x|<-4\) has no solution.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.