Chapter 9: Q12. (page 597)

Solve each equation by completing the square.
$x^{2} + 2 x + 5 = 0$

Short Answer

Expert verified

The quadratic equations have no real solutions.

Step by step solution

Step 1. Complete the square.

Complete the square to solve the quadratic equations by isolating $x^{2}$ andb-terms.

$x^{2} + 2 x + 5 = 0 x^{2} + 2 x + 5 + 1 = 0 + 1 [Since {(\frac{2}{2})}^{2} = 1 add to each side] x^{2} + 2 x + 1 + 5 - 5 = 1 - 5 [Subtract 5 to each side] x^{2} + 2 x + 1 = - 4$

Step 2. Take the square root of each side.

The first factor $x^{2} + 2 x + 1$ , then take the square root of each side.

width="400" height="54" role="math">(x+1)2=−4(x+1)2=±−4 Take the square root of each side

Step 3. Write the solutions.

No real number has a negative square. So, this equation $x^{2} + 2 x + 5 = 0$ has no real solutions.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each equation by completing the square.
$x^{2} + 2 x + 5 = 0$

Short Answer

Step by step solution

Step 1. Complete the square.

Step 2. Take the square root of each side.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Decision Maths

Calculus

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square.x2+2x+5=0

Short Answer

Step by step solution

Step 1. Complete the square.

Step 2. Take the square root of each side.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Decision Maths

Calculus

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square.
$x^{2} + 2 x + 5 = 0$