Q. 154 Solving quadratic equations12y2+... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 154 (page 899)

Solving quadratic equations
$12 y^{2} + 23 y = 24$ .
(a) by completing the square
(b) using the Quadratic Formula
(c) Which method do you prefer? Why?

Short Answer

Expert verified

The solutions of the equation

Part (a) by completing the square $\frac{3}{4} and - \frac{11}{6}$ .

Part (b) using the Quadratic Formula $\frac{3}{4} and - \frac{11}{6}$ .

Part (c) Quadratic formula.

Step by step solution

Step 1. Given information.

The given Quadratic equation is $12 y^{2} + 23 y = 24$ .

Part (a) Step 1. Factor the perfect square trinomial.

$12 y^{2} + 23 y = 24 12 (y^{2} + \frac{23}{12} y) = 12 路 2 y^{2} + \frac{23}{12} y = 2 y^{2} + \frac{23}{12} y + {(\frac{23}{24})}^{2} = 2 + \frac{529}{576} {(y + \frac{23}{24})}^{2} = \frac{1152 + 529}{576} y + \frac{23}{24} = 卤 \sqrt{\frac{1681}{576}} y + \frac{23}{24} = 卤 \frac{41}{24}$

Solve for y:

$y = \frac{41}{24} - \frac{23}{24} = \frac{41 - 23}{24} = \frac{18}{24} = \frac{3}{4}$ and $y = - \frac{41}{24} - \frac{23}{24} = \frac{- 41 - 23}{24} = - \frac{64}{24} = - \frac{11}{6}$

Part (b) Step 1. Using the Quadratic Formula.

$12^{2} + 23 y = 24$

Subtract 24 to get the equation in standard form.

$12 y^{2} + 23 y - 24 = 0$

Identify the values of a, b, and c.

$a = 12, b = 23, c = - 24$

Write the quadratic formula.

$y = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

Then substitute in the values of a, b, and c.

$y = \frac{- 23 卤 \sqrt{23^{2} - 4 路 12 路 (- 24)}}{2 路 12} y = \frac{- 23 卤 \sqrt{529 + 1152}}{24} y = \frac{- 23 卤 \sqrt{1681}}{24} y = \frac{- 23 卤 41}{24}$

Solve for y:

$y = \frac{- 23 + 41}{24} = \frac{18}{24} = \frac{3}{4}$ and $y = \frac{- 23 - 41}{24} = - \frac{64}{24} = - \frac{11}{6}$

Part (c) Step 1. Quadratic formula.

I prefer the quadratic formula because it it easy to use to finding the roots of the equations.

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solving quadratic equations
$12 y^{2} + 23 y = 24$ .
(a) by completing the square
(b) using the Quadratic Formula
(c) Which method do you prefer? Why?

Short Answer

Step by step solution

Step 1. Given information.

Part (a) Step 1. Factor the perfect square trinomial.

Part (b) Step 1. Using the Quadratic Formula.

Part (c) Step 1. Quadratic formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Logic and Functions

Probability and Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

Solving quadratic equations12y2+23y=24.(a) by completing the square(b) using the Quadratic Formula(c) Which method do you prefer? Why?

Short Answer

Step by step solution

Step 1. Given information.

Part (a) Step 1. Factor the perfect square trinomial.

Part (b) Step 1. Using the Quadratic Formula.

Part (c) Step 1. Quadratic formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Logic and Functions

Probability and Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solving quadratic equations
$12 y^{2} + 23 y = 24$ .
(a) by completing the square
(b) using the Quadratic Formula
(c) Which method do you prefer? Why?