If \(\frac{(4 x+3)^2}{2}=72\) and \(x>0\), then \(x=\)

Short Answer

Expert verified
So, when \(x > 0\), the value of \(x = \frac{9}{4}\).

Step by step solution

01

Multiply by 2

To eliminate the fraction, multiply both sides of the equation by 2: \[(4x+3)^2=144\]
02

Take the square root

Now, take the square root of both sides of the equation to get rid of the square: \[4x+3=\pm\sqrt{144}\] Since \(x>0\), we have: \[4x+3=12\]
03

Isolate x

Subtract 3 from both sides of the equation to isolate \(x\): \[4x=9\]
04

Solve for x

Finally, divide both sides of the equation by 4 to solve for \(x\): \[x=\frac{9}{4}\]

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 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

Laissez-faire is an economic environment in which transactions between private parties are largely free from government restrictions. Choose THREE characteristics that best exemplify laissez-faire economics: (a) Deregulation (b) Labor Laws (c) Building Codes (d) Free Trade (e) Antitrust Laws (f) Non-Interference

Why was the Berlin Airlift necessary? A. The Yalta Conference had impoverished the citizens of Berlin. B. The Marshall Plan had successfully assisted the citizens of Berlin to recover economically. C. The creation of the Warsaw Pact had prevented Berliners from accessing food supplies. D. The Soviets had closed supply routes to Berlin.

Which of the following best illustrates how the “wagon wheel” analogy applies to the U.S. system of government? A. A wagon wheel is one of four wheels needed to stabilize a wagon. B. The hub of a wagon wheel holds in place the spokes, which strengthen the structure of the wheel. C. A wagon wheel’s hub and spokes are made of different materials. D. A wagon wheel is created in several pieces and then assembled.

During periods that are unfavorable for growth, some plants become dormant. Woody plants are protected during such periods by their bark. Perennial plants die above ground, but their roots remain alive. Annual plants die, but their seeds survive to continue the life of the species. Which of the following would most likely be a time of year during which plants might lie dormant? A. winter B. spring C. summer D. fall

Which quotation from the story supports the idea that Ingred’s relatives have had military experience? A. “Mr. Saxon, Egbert, and Athelstane had only just been demobilized, and had hardly yet settled down to civilian life.” B. “The six weeks by the sea seemed a kind of oasis between the anxious period of the war that was past and gone, and the new epoch that stretched ahead in the future.” C. “By the by, now the war’s over, and we’ve all got our own again, I suppose you’re going back to Rotherwood, aren’t you?” D. “To have her father and brothers safely back, and for the family to be together in the midst of such beautiful scenery, was sufficient for utter enjoyment.”

See all solutions

Recommended explanations on English Textbooks

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