Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 111 E (page 886)

Solve the equation $x^{2} + 10 x = - 25$
$a$ by using the Square root property
$b$ by Completing the square
$c$ Which method do you prefer? Why?

Short Answer

Expert verified

The solution is $x = - 5$ . The preferred method is Completing the square .

Step by step solution

Part (a) Step 1. Given information

Equation: $x^{2} + 10 x = - 25$

Part (a) Step 2. Calculation

We have,

$x^{2} + 10 x = - 25$

$x^{2} + 10 x + {(\frac{1}{2} 路 (10))}^{2} = - 25 + {(\frac{1}{2} 路 (10))}^{2}$

$x^{2} + 10 x + 25 = - 25 + 25$

${(x + 5)}^{2} = 0$

localid="1645186040786" $\sqrt{{(x + 5)}^{2}} = \sqrt{0}$ using the Square root property

$x + 5 - 5 = 0 - 5$

$x = - 5$

Part (b) Step 1. Given information

Equation: $x^{2} + 10 x = - 25$

Part (b) Step 2. Calculation

We have,

$x^{2} + 10 x = - 25$

localid="1645185232165" $x^{2} + 10 x + {(\frac{1}{2} 路 (10))}^{2} = - 25 + {(\frac{1}{2} 路 (10))}^{2}$ using Completing the square

$x^{2} + 10 x + 25 = - 25 + 25$

localid="1645186141392" ${(x + 5)}^{2} = 0$

$\sqrt{{(x + 5)}^{2}} = \sqrt{0}$

$x + 5 - 5 = 0 - 5$

$x = - 5$

Part (c) Step 1. Explanation

I prefer Completing the square method since all quadratic equations can be solved by Completing the square. Whereas, Square root property is used to solve equations only when the left side is a perfect square.

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

Solve the equation $x^{2} + 10 x = - 25$
$a$ by using the Square root property
$b$ by Completing the square
$c$ Which method do you prefer? Why?

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 1. Given information

Part (b) Step 2. Calculation

Part (c) Step 1. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Calculus

Probability and Statistics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Solve the equationx2+10x=-25aby using the Square root propertybby Completing the squarec Which method do you prefer? Why?

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 1. Given information

Part (b) Step 2. Calculation

Part (c) Step 1. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Calculus

Probability and Statistics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the equation $x^{2} + 10 x = - 25$
$a$ by using the Square root property
$b$ by Completing the square
$c$ Which method do you prefer? Why?