/*! 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 31 Solve each equation. $$36=25 n... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 31

Solve each equation. $$36=25 n^{2}$$

Short Answer

Expert verified
The solution to the equation \(36 = 25n^2\) is \(n = \frac{6}{5}\) and \(n = -\frac{6}{5}\).

Step by step solution

01

Isolate the n-squared term

Divide both sides of the equation by 25 in order to isolate the n-squared term: \[ \frac{36}{25} = n^2 \]
02

Take the square root of both sides

To find the value of n, we need to take the square root of both sides of the equation: \[ \sqrt{\frac{36}{25}} = \sqrt{n^2} \]
03

Simplify and solve for n

Now, we simplify the equation and find the value of n: \[ \frac{\sqrt{36}}{\sqrt{25}} = n \] Since 36 has two square roots, 卤6, and 25 has one square root, 5, we have: \[ n = \frac{卤6}{5} \] So, there are two possible values for n: \[ n = \frac{6}{5}, n = -\frac{6}{5} \]

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solving Equations
To solve an equation like the one given, we need to find the values of the variable that make the equation true. The equation provided is a basic example of a quadratic equation: \(36 = 25n^2\). Our goal is to isolate the variable \(n\). This means we want \(n\) on one side of the equation and everything else on the other.
  • Start by adjusting the equation so \(n^2\) is by itself. In this case, divide both sides by 25.
  • Mathematically, this step rearranges our equation to \(\frac{36}{25} = n^2\).
When solving equations, each step you take is intended to simplify down to the variable you are interested in. Keep your operations equal on both sides to retain a balanced equation, leading you steadily to the solution. Adjusting equations involves basic operations like addition, subtraction, multiplication, division, and other algebraic manipulations.
Square Roots
The next step involves understanding square roots. A square root asks the question, "What number multiplied by itself gives me this number?" For the equation \(n^2 = \frac{36}{25}\), solving for \(n\) requires us to find the square root of both sides.
  • The square root of \(n^2\) is \(n\), because \(n \times n = n^2\).
  • For the fraction \(\frac{36}{25}\), take the square root of each part separately: \(\sqrt{36} = 6\) and \(\sqrt{25} = 5\).
This step simplifies the equation to \(n = \pm \frac{6}{5}\). Using square roots introduces the concept of two solutions: a positive and a negative outcome. In quadratic equations, this is because both \(x\) and \(-x\) would give the original squared value when squared.
Algebraic Expressions
The given problem also highlights working with algebraic expressions, where understanding how to manipulate and simplify expressions is crucial. An algebraic expression includes variables, constants, and operations which you can rearrange and solve.In our example \(\frac{36}{25} = n^2\), the expression on the left side is a fraction. Working with fractions includes:
  • Understanding numerators and denominators, like 36 (numerator) and 25 (denominator).
  • Using square roots effectively by recognizing that each part can be separately simplified: \(\frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5}\).
When solving algebraic expressions, practice breaking down each term and operation. Each small step clarifies the path to the final variable solution. Keep in mind that algebra is like a puzzle, and each piece fits together logically to produce the answer.

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

Factor completely by first taking out a negative common factor. $$-6 c^{3} d+27 c^{2} d^{2}-12 c d^{3}$$

Factor completely. $$d^{3}+1$$

Henry and Allison leave home to go to work. Henry drives due west while his wife drives due south. At 8: 30 am, Allison is 3 mi farther from home than Henry, and the distance between them is 6 mi more than Henry's distance from home. Find Henry's distance from his house.

Factor completely. $$z^{3}-1000$$

Write an equation and solve. A rectangular aquarium is 15 in. high, and its length is 8 in. more than its width. Find the length and width if the volume of the aquarium is 3600 in \(^{3}\).
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

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.