Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 15

If \(2 \sqrt{x}=x-3\), which of the following is the solution set for \(x\) ? A) \(\\{-1,9\\}\) B) \(\\{1,-9\\}\) C) \(\\{9\\}\) D) \(\\{1,9\\}\)

Short Answer

Expert verified
The correct solution set for the given equation is C) \(\{9\}\).

Step by step solution

01

Square both sides of the equation

To eliminate the square root, square both sides of the equation \(2 \sqrt{x}=x-3\). This will give the equation: \[(2\sqrt{x})^2 = (x-3)^2.\]
02

Simplify the equation

Simplify both sides of the equation from the previous step. On the left side, the square and the square root will cancel out: \[(2\sqrt{x})^2 = 4x,\] while on the right side, expand the binomial: \[(x-3)^2 = x^2 - 6x + 9.\] This results in the equation: \[4x = x^2 - 6x + 9.\]
03

Rearrange and Solve the Quadratic Equation

To solve for x, move all terms to one side of the equation, creating a quadratic equation: \[x^2 - 10x + 9 = 0.\] Now, attempt to factor this quadratic equation: \[(x - 1)(x - 9)= 0\] The solutions for x are 1 and 9: \[x=1, x=9.\]
04

Verify the solutions

To verify whether the solutions are valid, plug each solution back into the original equation: For x = 1: \(2 \sqrt{1}=1-3\) gives \(2 \neq -2\). In this case, \(x=1\) is not a valid solution. For x = 9: \(2 \sqrt{9}=9-3\) gives \(6=6\). In this case, \(x=9\) is a valid solution. So, the correct solution set for the given equation is \(\{9\}\). The correct answer is: C) \(\{9\}\).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

If \(18+d=12\), what is the value of \(5 d\) ? A) \(-30\) B) \(-18\) C) \(-6\) D) 6

Which of the following is equivalent to \(9 y^4+6 y^3+3\) ? A) \(3 y^2\left(3 y^2+6 y+3\right)\) B) \(3 y^2\left(3 y^2+2 y\right)+3\) C) \(3 y^2\left(6 y^2+3 y+1\right)\) D) \(15 y^7+3\)

The principal at a large high school in a major city believes that the math teachers for each class assign drastically different amounts of homework to their respective students. Which method of sampling would be best to estimate the average number of hours of homework assigned to students by the different math teachers? A) Select one math teacher at random and survey the number of assigned homework hours in each of his or her classes. B) Post an online poll to the school's social media account that asks students how much math homework they get each night. C) Select 5 students from each math class in the high school and then record the number of hours assigned to each student selected. D) Select the student with the highest grade in each math class and then survey those students to see how much homework they do each night.

If \(x^2+2 x y+y^2=64\) and \(y-x=12\), which of the following could be the value of \(x\) ? A) \(-10\) B) \(-4\) C) 2 D) 10

The primary purpose of the passage is to A) support the findings of classic laboratory experimentation. B) assert that controversial findings should cause alarm. C) present concerns raised by the results of a study. D) criticize the methodology of an existing study.
See all solutions

Recommended explanations on English Textbooks

Essay Prompts

Read Explanation

Creative Story

Read Explanation

Language and Social Groups

Read Explanation

Phonetics

Read Explanation

5 Paragraph Essay

Read Explanation

Essay Writing Skills

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.

Sign-up for free