/*! 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 2 Solve the following quadratic eq... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 2

Solve the following quadratic equations. \(b^{2}=144\)

Short Answer

Expert verified
The solutions are \( b = 12 \) and \( b = -12 \).

Step by step solution

01

- Understand the equation

The equation given is a quadratic equation: \( b^2 = 144 \). This represents a simple quadratic equation in the form of \( x^2 = c \).
02

- Isolate the variable

To find the value of \( b \), take the square root of both sides of the equation. This will give two possible solutions because both positive and negative numbers squared give the same result.
03

- Calculate the square roots

Calculate the square root of 144: \[ b = \pm \sqrt{144} \]. The square root of 144 is 12, so the solutions are \( b = 12 \) and \( b = -12 \).
04

- State the solutions

So, the solutions to the quadratic equation \( b^2 = 144 \) are \( b = 12 \) and \( b = -12 \).

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 Quadratic Equations
Quadratic equations are mathematical expressions of the form \(ax^2 + bx + c = 0\). They often pop up in various areas of algebra and geometry. In this exercise, you encountered a simplified quadratic equation: \(b^2 = 144\). Solving such equations involves finding the value of the variable鈥攊n this case, \b\鈥攖hat makes the equation true. Let's break it down further.
Square Roots
Square roots are key to solving many algebraic equations, especially quadratics. A square root of a number \x\ is a value that, when multiplied by itself, yields \x\. For example, the square root of 144 is 12 because \(12 \times 12 = 144\).
Positive and Negative Solutions
In quadratic equations, every solution has a 'twin'鈥攊ts positive and negative counterpart. This means that for any \x^2 = c\, you'll find both \sqrt{c}\ and \-\sqrt{c}\ as solutions. The initial example of \(b^2 = 144\) perfectly illustrates this concept.

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

The product of two consecutive odd numbers is 255 . Find the numbers.

The product of two consecutive even numbers is 624 . Find the numbers.

Solve by using the Quadratic Formula. \(5 b^{2}+2 b-4=0\)

Yvette wants to put a square swimming pool in the corner of her backyard. She will have a 3 foot deck on the south side of the pool and a 9 foot deck on the west side of the pool. She has a total area of 1080 square feet for the pool and two decks. Solve the equation \((s+3)(s+9)=1080\) for \(s,\) the length of a side of the pool.

The width of a triangle is six more than twice the height. The area of the triangle is 88 square yards. Find the height and width of the triangle.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics 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.